- Problems & Exercises
- Introduction to Science and the Realm of Physics, Physical Quantities, and Units
- 1.1 Physics: An Introduction

1.2 Physical Quantities and Units
1.3 accuracy, precision, and significant figures, 1.4 approximation.
- Section Summary
- Conceptual Questions
- Introduction to One-Dimensional Kinematics
- 2.1 Displacement
- 2.2 Vectors, Scalars, and Coordinate Systems
- 2.3 Time, Velocity, and Speed
- 2.4 Acceleration
- 2.5 Motion Equations for Constant Acceleration in One Dimension
- 2.6 Problem-Solving Basics for One-Dimensional Kinematics
- 2.7 Falling Objects
- 2.8 Graphical Analysis of One-Dimensional Motion
- Introduction to Two-Dimensional Kinematics
- 3.1 Kinematics in Two Dimensions: An Introduction
- 3.2 Vector Addition and Subtraction: Graphical Methods
- 3.3 Vector Addition and Subtraction: Analytical Methods
- 3.4 Projectile Motion
- 3.5 Addition of Velocities
- Introduction to Dynamics: Newton’s Laws of Motion
- 4.1 Development of Force Concept
- 4.2 Newton’s First Law of Motion: Inertia
- 4.3 Newton’s Second Law of Motion: Concept of a System
- 4.4 Newton’s Third Law of Motion: Symmetry in Forces
- 4.5 Normal, Tension, and Other Examples of Forces
- 4.6 Problem-Solving Strategies
- 4.7 Further Applications of Newton’s Laws of Motion
- 4.8 Extended Topic: The Four Basic Forces—An Introduction
- Introduction: Further Applications of Newton’s Laws
- 5.1 Friction
- 5.2 Drag Forces
- 5.3 Elasticity: Stress and Strain
- Introduction to Uniform Circular Motion and Gravitation
- 6.1 Rotation Angle and Angular Velocity
- 6.2 Centripetal Acceleration
- 6.3 Centripetal Force
- 6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force
- 6.5 Newton’s Universal Law of Gravitation
- 6.6 Satellites and Kepler’s Laws: An Argument for Simplicity
- Introduction to Work, Energy, and Energy Resources
- 7.1 Work: The Scientific Definition
- 7.2 Kinetic Energy and the Work-Energy Theorem
- 7.3 Gravitational Potential Energy
- 7.4 Conservative Forces and Potential Energy
- 7.5 Nonconservative Forces
- 7.6 Conservation of Energy
- 7.8 Work, Energy, and Power in Humans
- 7.9 World Energy Use
- Introduction to Linear Momentum and Collisions
- 8.1 Linear Momentum and Force
- 8.2 Impulse
- 8.3 Conservation of Momentum
- 8.4 Elastic Collisions in One Dimension
- 8.5 Inelastic Collisions in One Dimension
- 8.6 Collisions of Point Masses in Two Dimensions
- 8.7 Introduction to Rocket Propulsion
- Introduction to Statics and Torque
- 9.1 The First Condition for Equilibrium
- 9.2 The Second Condition for Equilibrium
- 9.3 Stability
- 9.4 Applications of Statics, Including Problem-Solving Strategies
- 9.5 Simple Machines
- 9.6 Forces and Torques in Muscles and Joints
- Introduction to Rotational Motion and Angular Momentum
- 10.1 Angular Acceleration
- 10.2 Kinematics of Rotational Motion
- 10.3 Dynamics of Rotational Motion: Rotational Inertia
- 10.4 Rotational Kinetic Energy: Work and Energy Revisited
- 10.5 Angular Momentum and Its Conservation
- 10.6 Collisions of Extended Bodies in Two Dimensions
- 10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum
- Introduction to Fluid Statics
- 11.1 What Is a Fluid?
- 11.2 Density
- 11.3 Pressure
- 11.4 Variation of Pressure with Depth in a Fluid
- 11.5 Pascal’s Principle
- 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement
- 11.7 Archimedes’ Principle
- 11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action
- 11.9 Pressures in the Body
- Introduction to Fluid Dynamics and Its Biological and Medical Applications
- 12.1 Flow Rate and Its Relation to Velocity
- 12.2 Bernoulli’s Equation
- 12.3 The Most General Applications of Bernoulli’s Equation
- 12.4 Viscosity and Laminar Flow; Poiseuille’s Law
- 12.5 The Onset of Turbulence
- 12.6 Motion of an Object in a Viscous Fluid
- 12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes
- Introduction to Temperature, Kinetic Theory, and the Gas Laws
- 13.1 Temperature
- 13.2 Thermal Expansion of Solids and Liquids
- 13.3 The Ideal Gas Law
- 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
- 13.5 Phase Changes
- 13.6 Humidity, Evaporation, and Boiling
- Introduction to Heat and Heat Transfer Methods
- 14.2 Temperature Change and Heat Capacity
- 14.3 Phase Change and Latent Heat
- 14.4 Heat Transfer Methods
- 14.5 Conduction
- 14.6 Convection
- 14.7 Radiation
- Introduction to Thermodynamics
- 15.1 The First Law of Thermodynamics
- 15.2 The First Law of Thermodynamics and Some Simple Processes
- 15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
- 15.4 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated
- 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators
- 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy
- 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation
- Introduction to Oscillatory Motion and Waves
- 16.1 Hooke’s Law: Stress and Strain Revisited
- 16.2 Period and Frequency in Oscillations
- 16.3 Simple Harmonic Motion: A Special Periodic Motion
- 16.4 The Simple Pendulum
- 16.5 Energy and the Simple Harmonic Oscillator
- 16.6 Uniform Circular Motion and Simple Harmonic Motion
- 16.7 Damped Harmonic Motion
- 16.8 Forced Oscillations and Resonance
- 16.10 Superposition and Interference
- 16.11 Energy in Waves: Intensity
- Introduction to the Physics of Hearing
- 17.2 Speed of Sound, Frequency, and Wavelength
- 17.3 Sound Intensity and Sound Level
- 17.4 Doppler Effect and Sonic Booms
- 17.5 Sound Interference and Resonance: Standing Waves in Air Columns
- 17.6 Hearing
- 17.7 Ultrasound
- Introduction to Electric Charge and Electric Field
- 18.1 Static Electricity and Charge: Conservation of Charge
- 18.2 Conductors and Insulators
- 18.3 Coulomb’s Law
- 18.4 Electric Field: Concept of a Field Revisited
- 18.5 Electric Field Lines: Multiple Charges
- 18.6 Electric Forces in Biology
- 18.7 Conductors and Electric Fields in Static Equilibrium
- 18.8 Applications of Electrostatics
- Introduction to Electric Potential and Electric Energy
- 19.1 Electric Potential Energy: Potential Difference
- 19.2 Electric Potential in a Uniform Electric Field
- 19.3 Electrical Potential Due to a Point Charge
- 19.4 Equipotential Lines
- 19.5 Capacitors and Dielectrics
- 19.6 Capacitors in Series and Parallel
- 19.7 Energy Stored in Capacitors
- Introduction to Electric Current, Resistance, and Ohm's Law
- 20.1 Current
- 20.2 Ohm’s Law: Resistance and Simple Circuits
- 20.3 Resistance and Resistivity
- 20.4 Electric Power and Energy
- 20.5 Alternating Current versus Direct Current
- 20.6 Electric Hazards and the Human Body
- 20.7 Nerve Conduction–Electrocardiograms
- Introduction to Circuits and DC Instruments
- 21.1 Resistors in Series and Parallel
- 21.2 Electromotive Force: Terminal Voltage
- 21.3 Kirchhoff’s Rules
- 21.4 DC Voltmeters and Ammeters
- 21.5 Null Measurements
- 21.6 DC Circuits Containing Resistors and Capacitors
- Introduction to Magnetism
- 22.1 Magnets
- 22.2 Ferromagnets and Electromagnets
- 22.3 Magnetic Fields and Magnetic Field Lines
- 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
- 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
- 22.6 The Hall Effect
- 22.7 Magnetic Force on a Current-Carrying Conductor
- 22.8 Torque on a Current Loop: Motors and Meters
- 22.9 Magnetic Fields Produced by Currents: Ampere’s Law
- 22.10 Magnetic Force between Two Parallel Conductors
- 22.11 More Applications of Magnetism
- Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies
- 23.1 Induced Emf and Magnetic Flux
- 23.2 Faraday’s Law of Induction: Lenz’s Law
- 23.3 Motional Emf
- 23.4 Eddy Currents and Magnetic Damping
- 23.5 Electric Generators
- 23.6 Back Emf
- 23.7 Transformers
- 23.8 Electrical Safety: Systems and Devices
- 23.9 Inductance
- 23.10 RL Circuits
- 23.11 Reactance, Inductive and Capacitive
- 23.12 RLC Series AC Circuits
- Introduction to Electromagnetic Waves
- 24.1 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
- 24.2 Production of Electromagnetic Waves
- 24.3 The Electromagnetic Spectrum
- 24.4 Energy in Electromagnetic Waves
- Introduction to Geometric Optics
- 25.1 The Ray Aspect of Light
- 25.2 The Law of Reflection
- 25.3 The Law of Refraction
- 25.4 Total Internal Reflection
- 25.5 Dispersion: The Rainbow and Prisms
- 25.6 Image Formation by Lenses
- 25.7 Image Formation by Mirrors
- Introduction to Vision and Optical Instruments
- 26.1 Physics of the Eye
- 26.2 Vision Correction
- 26.3 Color and Color Vision
- 26.4 Microscopes
- 26.5 Telescopes
- 26.6 Aberrations
- Introduction to Wave Optics
- 27.1 The Wave Aspect of Light: Interference
- 27.2 Huygens's Principle: Diffraction
- 27.3 Young’s Double Slit Experiment
- 27.4 Multiple Slit Diffraction
- 27.5 Single Slit Diffraction
- 27.6 Limits of Resolution: The Rayleigh Criterion
- 27.7 Thin Film Interference
- 27.8 Polarization
- 27.9 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light
- Introduction to Special Relativity
- 28.1 Einstein’s Postulates
- 28.2 Simultaneity And Time Dilation
- 28.3 Length Contraction
- 28.4 Relativistic Addition of Velocities
- 28.5 Relativistic Momentum
- 28.6 Relativistic Energy
- Introduction to Quantum Physics
- 29.1 Quantization of Energy
- 29.2 The Photoelectric Effect
- 29.3 Photon Energies and the Electromagnetic Spectrum
- 29.4 Photon Momentum
- 29.5 The Particle-Wave Duality
- 29.6 The Wave Nature of Matter
- 29.7 Probability: The Heisenberg Uncertainty Principle
- 29.8 The Particle-Wave Duality Reviewed
- Introduction to Atomic Physics
- 30.1 Discovery of the Atom
- 30.2 Discovery of the Parts of the Atom: Electrons and Nuclei
- 30.3 Bohr’s Theory of the Hydrogen Atom
- 30.4 X Rays: Atomic Origins and Applications
- 30.5 Applications of Atomic Excitations and De-Excitations
- 30.6 The Wave Nature of Matter Causes Quantization
- 30.7 Patterns in Spectra Reveal More Quantization
- 30.8 Quantum Numbers and Rules
- 30.9 The Pauli Exclusion Principle
- Introduction to Radioactivity and Nuclear Physics
- 31.1 Nuclear Radioactivity
- 31.2 Radiation Detection and Detectors
- 31.3 Substructure of the Nucleus
- 31.4 Nuclear Decay and Conservation Laws
- 31.5 Half-Life and Activity
- 31.6 Binding Energy
- 31.7 Tunneling
- Introduction to Applications of Nuclear Physics
- 32.1 Medical Imaging and Diagnostics
- 32.2 Biological Effects of Ionizing Radiation
- 32.3 Therapeutic Uses of Ionizing Radiation
- 32.4 Food Irradiation
- 32.5 Fusion
- 32.6 Fission
- 32.7 Nuclear Weapons
- Introduction to Particle Physics
- 33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited
- 33.2 The Four Basic Forces
- 33.3 Accelerators Create Matter from Energy
- 33.4 Particles, Patterns, and Conservation Laws
- 33.5 Quarks: Is That All There Is?
- 33.6 GUTs: The Unification of Forces
- Introduction to Frontiers of Physics
- 34.1 Cosmology and Particle Physics
- 34.2 General Relativity and Quantum Gravity
- 34.3 Superstrings
- 34.4 Dark Matter and Closure
- 34.5 Complexity and Chaos
- 34.6 High-temperature Superconductors
- 34.7 Some Questions We Know to Ask
- A | Atomic Masses
- B | Selected Radioactive Isotopes
- C | Useful Information
- D | Glossary of Key Symbols and Notation
The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?
A car is traveling at a speed of 33 m/s 33 m/s size 12{"33"" m/s"} {} . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h 90 km/h size 12{"90"" km/h"} {} speed limit?
Show that 1 . 0 m/s = 3 . 6 km/h 1 . 0 m/s = 3 . 6 km/h size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {} . Hint: Show the explicit steps involved in converting 1 . 0 m/s = 3 . 6 km/h. 1 . 0 m/s = 3 . 6 km/h. size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {}
American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)
Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)
What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)
Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)
The speed of sound is measured to be 342 m/s 342 m/s size 12{"342"" m/s"} {} on a certain day. What is this in km/h?
Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?
(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?
Express your answers to problems in this section to the correct number of significant figures and proper units.
Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?
A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?
(a) A car speedometer has a 5.0 % 5.0 % size 12{5.0%} {} uncertainty. What is the range of possible speeds when it reads 90 km/h 90 km/h size 12{"90"" km/h"} {} ? (b) Convert this range to miles per hour. 1 km = 0.6214 mi 1 km = 0.6214 mi size 12{"1 km" "=" "0.6214 mi"} {}
An infant’s pulse rate is measured to be 130 ± 5 130 ± 5 size 12{"130" +- 5} {} beats/min. What is the percent uncertainty in this measurement?
(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?
A can contains 375 mL of soda. How much is left after 308 mL is removed?
State how many significant figures are proper in the results of the following calculations: (a) 106 . 7 98 . 2 / 46 . 210 1 . 01 106 . 7 98 . 2 / 46 . 210 1 . 01 size 12{ left ("106" "." 7 right ) left ("98" "." 2 right )/ left ("46" "." "210" right ) left (1 "." "01" right )} {} (b) 18 . 7 2 18 . 7 2 size 12{ left ("18" "." 7 right ) rSup { size 8{2} } } {} (c) 1 . 60 × 10 − 19 3712 1 . 60 × 10 − 19 3712 size 12{ left (1 "." "60" times "10" rSup { size 8{ - "19"} } right ) left ("3712" right )} {} .
(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?
(a) If your speedometer has an uncertainty of 2 . 0 km/h 2 . 0 km/h size 12{2 "." 0" km/h"} {} at a speed of 90 km/h 90 km/h size 12{"90"" km/h"} {} , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h 60 km/h size 12{"60"" km/h"} {} , what is the range of speeds you could be going?
(a) A person’s blood pressure is measured to be 120 ± 2 mm Hg 120 ± 2 mm Hg size 12{"120" +- 2" mm Hg"} {} . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg 80 mm Hg size 12{"80"" mm Hg"} {} ?
A person measures his or her heart rate by counting the number of beats in 30 s 30 s size 12{"30"" s"} {} . If 40 ± 1 40 ± 1 size 12{"40" +- 1} {} beats are counted in 30 . 0 ± 0 . 5 s 30 . 0 ± 0 . 5 s size 12{"30" "." 0 +- 0 "." 5" s"} {} , what is the heart rate and its uncertainty in beats per minute?
What is the area of a circle 3 . 102 cm 3 . 102 cm size 12{3 "." "102"" cm"} {} in diameter?
If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?
A marathon runner completes a 42 . 188 -km 42 . 188 -km size 12{"42" "." "188""-km"} {} course in 2 h 2 h size 12{2" h"} {} , 30 min, and 12 s 12 s size 12{"12"" s"} {} . There is an uncertainty of 25 m 25 m size 12{"25"" m"} {} in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?
The sides of a small rectangular box are measured to be 1 . 80 ± 0 . 01 cm 1 . 80 ± 0 . 01 cm size 12{1 "." "80" +- 0 "." "01"" cm"} {} , {} 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm size 12{2 "." "05" +- 0 "." "02"" cm, and 3" "." 1 +- 0 "." "1 cm"} {} long. Calculate its volume and uncertainty in cubic centimeters.
When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0 . 4539 kg 1 lbm = 0 . 4539 kg size 12{1" lbm"=0 "." "4539"`"kg"} {} . (a) If there is an uncertainty of 0 . 0001 kg 0 . 0001 kg size 12{0 "." "0001"`"kg"} {} in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?
The length and width of a rectangular room are measured to be 3 . 955 ± 0 . 005 m 3 . 955 ± 0 . 005 m size 12{3 "." "955" +- 0 "." "005"" m"} {} and 3 . 050 ± 0 . 005 m 3 . 050 ± 0 . 005 m size 12{3 "." "050" +- 0 "." "005"" m"} {} . Calculate the area of the room and its uncertainty in square meters.
A car engine moves a piston with a circular cross section of 7 . 500 ± 0 . 002 cm 7 . 500 ± 0 . 002 cm size 12{7 "." "500" +- 0 "." "002"`"cm"} {} diameter a distance of 3 . 250 ± 0 . 001 cm 3 . 250 ± 0 . 001 cm size 12{3 "." "250" +- 0 "." "001"`"cm"} {} to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.
How many heartbeats are there in a lifetime?
A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?
How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10 − 22 s 10 − 22 s size 12{"10" rSup { size 8{ - "22"} } " s"} {} .)
Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10 − 27 kg 10 − 27 kg size 12{"10" rSup { size 8{ - "27"} } " kg"} {} and the mass of a bacterium is on the order of 10 − 15 kg. 10 − 15 kg. size 12{"10" rSup { size 8{ - "15"} } "kg"} {} )
Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?
(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?
(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?
Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?
As an Amazon Associate we earn from qualifying purchases.
Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.
Access for free at https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
- Authors: Paul Peter Urone, Roger Hinrichs
- Publisher/website: OpenStax
- Book title: College Physics
- Publication date: Jun 21, 2012
- Location: Houston, Texas
- Book URL: https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
- Section URL: https://openstax.org/books/college-physics/pages/1-problems-exercises
© Mar 3, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Physics Problems with Solutions
Physics problems with solutions and tutorials.
Please enable JavaScript

Popular Pages
- For a new problem, you will need to begin a new live expert session.
- You can contact support with any questions regarding your current subscription.
- You will be able to enter math problems once our session is over.
- I am only able to help with one math problem per session. Which problem would you like to work on?
- Does that make sense?
- I am currently working on this problem.
- Are you still there?
- It appears we may have a connection issue. I will end the session - please reconnect if you still need assistance.
- Let me take a look...
- Can you please send an image of the problem you are seeing in your book or homework?
- If you click on "Tap to view steps..." you will see the steps are now numbered. Which step # do you have a question on?
- Please make sure you are in the correct subject. To change subjects, please exit out of this live expert session and select the appropriate subject from the menu located in the upper left corner of the Mathway screen.
- What are you trying to do with this input?
- While we cover a very wide range of problems, we are currently unable to assist with this specific problem. I spoke with my team and we will make note of this for future training. Is there a different problem you would like further assistance with?
- Mathway currently does not support this subject. We are more than happy to answer any math specific question you may have about this problem.
- Mathway currently does not support Ask an Expert Live in Chemistry. If this is what you were looking for, please contact support.
- Mathway currently only computes linear regressions.
- We are here to assist you with your math questions. You will need to get assistance from your school if you are having problems entering the answers into your online assignment.
- Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.
- Have a great day!
- Hope that helps!
- You're welcome!
- Per our terms of use, Mathway's live experts will not knowingly provide solutions to students while they are taking a test or quiz.
Please ensure that your password is at least 8 characters and contains each of the following:
- a special character: @$#!%*?&

- TPC and eLearning
- Read Watch Interact
- What's NEW at TPC?
- Practice Review Test
- Teacher-Tools
- Subscription Selection
- Seat Calculator
- Ad Free Account
- Student Progress Edit
- Task Properties
- Export Student Progress
- Task, Activities, and Scores
- Edit Profile Settings
- Tasks and Courses
- Subscription
- Subscription Locator
- Metric Conversions Questions
- Metric System Questions
- Metric Estimation Questions
- Significant Digits Questions
- Proportional Reasoning
- Acceleration
- Distance-Displacement
- Dots and Graphs
- Graph That Motion
- Match That Graph
- Name That Motion
- Motion Diagrams
- Pos'n Time Graphs Numerical
- Pos'n Time Graphs Conceptual
- Up And Down - Questions
- Balanced vs. Unbalanced Forces
- Change of State
- Force and Motion
- Mass and Weight
- Match That Free-Body Diagram
- Net Force (and Acceleration) Ranking Tasks
- Newton's Second Law
- Normal Force Card Sort
- Recognizing Forces
- Air Resistance and Skydiving
- Solve It! with Newton's Second Law
- Which One Doesn't Belong?
- Component Addition Questions
- Head-to-Tail Vector Addition
- Projectile Mathematics
- Trajectory - Angle Launched Projectiles
- Trajectory - Horizontally Launched Projectiles
- Vector Addition
- Vector Direction
- Which One Doesn't Belong? Projectile Motion
- Forces in 2-Dimensions
- Being Impulsive About Momentum
- Explosions - Law Breakers
- Hit and Stick Collisions - Law Breakers
- Case Studies: Impulse and Force
- Impulse-Momentum Change Table
- Keeping Track of Momentum - Hit and Stick
- Keeping Track of Momentum - Hit and Bounce
- What's Up (and Down) with KE and PE?
- Energy Conservation Questions
- Energy Dissipation Questions
- Energy Ranking Tasks
- LOL Charts (a.k.a., Energy Bar Charts)
- Match That Bar Chart
- Words and Charts Questions
- Name That Energy
- Stepping Up with PE and KE Questions
- Case Studies - Circular Motion
- Circular Logic
- Forces and Free-Body Diagrams in Circular Motion
- Gravitational Field Strength
- Universal Gravitation
- Angular Position and Displacement
- Linear and Angular Velocity
- Getting a Handle on Torque
- Torque-ing About Rotation
- Balloon Interactions
- Charge and Charging
- Charge Interactions
- Charging by Induction
- Conductors and Insulators
- Coulombs Law
- Electric Field
- Electric Field Intensity
- Polarization
- Case Studies: Electric Power
- Know Your Potential
- Light Bulb Anatomy
- I = ∆V/R Equations as a Guide to Thinking
- Parallel Circuits - ∆V = I•R Calculations
- Resistance Ranking Tasks
- Series Circuits - ∆V = I•R Calculations
- Series vs. Parallel Circuits
- Equivalent Resistance
- Period and Frequency of a Pendulum
- Pendulum Motion: Velocity and Force
- Energy of a Pendulum
- Period and Frequency of a Mass on a Spring
- Horizontal Springs: Velocity and Force
- Vertical Springs: Velocity and Force
- Energy of a Mass on a Spring
- Decibel Scale
- Frequency and Period
- Closed-End Air Columns
- Name That Harmonic: Strings
- Rocking the Boat
- Wave Basics
- Matching Pairs: Wave Characteristics
- Wave Interference
- Waves - Case Studies
- Color Addition and Subtraction
- Color Filters
- If This, Then That: Color Subtraction
- Light Intensity
- Color Pigments
- Converging Lenses
- Curved Mirror Images
- Law of Reflection
- Refraction and Lenses
- Total Internal Reflection
- Who Can See Who?
- Formulas and Atom Counting
- Atomic Models
- Bond Polarity
- Entropy Questions
- Cell Voltage Questions
- Heat of Formation Questions
- Reduction Potential Questions
- Oxidation States Questions
- Measuring the Quantity of Heat
- Hess's Law
- Oxidation-Reduction Questions
- Galvanic Cells Questions
- Thermal Stoichiometry
- Molecular Polarity
- Quantum Mechanics
- Balancing Chemical Equations
- Bronsted-Lowry Model of Acids and Bases
- Classification of Matter
- Collision Model of Reaction Rates
- Density Ranking Tasks
- Dissociation Reactions
- Complete Electron Configurations
- Enthalpy Change Questions
- Equilibrium Concept
- Equilibrium Constant Expression
- Equilibrium Calculations - Questions
- Equilibrium ICE Table
- Ionic Bonding
- Lewis Electron Dot Structures
- Line Spectra Questions
- Measurement and Numbers
- Metals, Nonmetals, and Metalloids
- Metric Estimations
- Metric System
- Molarity Ranking Tasks
- Mole Conversions
- Name That Element
- Names to Formulas
- Names to Formulas 2
- Nuclear Decay
- Particles, Words, and Formulas
- Periodic Trends
- Precipitation Reactions and Net Ionic Equations
- Pressure Concepts
- Pressure-Temperature Gas Law
- Pressure-Volume Gas Law
- Chemical Reaction Types
- Significant Digits and Measurement
- States Of Matter Exercise
- Stoichiometry - Math Relationships
- Subatomic Particles
- Spontaneity and Driving Forces
- Gibbs Free Energy
- Volume-Temperature Gas Law
- Acid-Base Properties
- Energy and Chemical Reactions
- Chemical and Physical Properties
- Valence Shell Electron Pair Repulsion Theory
- Writing Balanced Chemical Equations
- Mission CG1
- Mission CG10
- Mission CG2
- Mission CG3
- Mission CG4
- Mission CG5
- Mission CG6
- Mission CG7
- Mission CG8
- Mission CG9
- Mission EC1
- Mission EC10
- Mission EC11
- Mission EC12
- Mission EC2
- Mission EC3
- Mission EC4
- Mission EC5
- Mission EC6
- Mission EC7
- Mission EC8
- Mission EC9
- Mission RL1
- Mission RL2
- Mission RL3
- Mission RL4
- Mission RL5
- Mission RL6
- Mission KG7
- Mission RL8
- Mission KG9
- Mission RL10
- Mission RL11
- Mission RM1
- Mission RM2
- Mission RM3
- Mission RM4
- Mission RM5
- Mission RM6
- Mission RM8
- Mission RM10
- Mission LC1
- Mission RM11
- Mission LC2
- Mission LC3
- Mission LC4
- Mission LC5
- Mission LC6
- Mission LC8
- Mission SM1
- Mission SM2
- Mission SM3
- Mission SM4
- Mission SM5
- Mission SM6
- Mission SM8
- Mission SM10
- Mission KG10
- Mission SM11
- Mission KG2
- Mission KG3
- Mission KG4
- Mission KG5
- Mission KG6
- Mission KG8
- Mission KG11
- Mission F2D1
- Mission F2D2
- Mission F2D3
- Mission F2D4
- Mission F2D5
- Mission F2D6
- Mission KC1
- Mission KC2
- Mission KC3
- Mission KC4
- Mission KC5
- Mission KC6
- Mission KC7
- Mission KC8
- Mission AAA
- Mission SM9
- Mission LC7
- Mission LC9
- Mission NL1
- Mission NL2
- Mission NL3
- Mission NL4
- Mission NL5
- Mission NL6
- Mission NL7
- Mission NL8
- Mission NL9
- Mission NL10
- Mission NL11
- Mission NL12
- Mission MC1
- Mission MC10
- Mission MC2
- Mission MC3
- Mission MC4
- Mission MC5
- Mission MC6
- Mission MC7
- Mission MC8
- Mission MC9
- Mission RM7
- Mission RM9
- Mission RL7
- Mission RL9
- Mission SM7
- Mission SE1
- Mission SE10
- Mission SE11
- Mission SE12
- Mission AAA2
- Mission SE4
- Mission SE5
- Mission SE6
- Mission SE7
- Mission SE8
- Mission SE9
- Mission VP1
- Mission VP10
- Mission VP2
- Mission VP3
- Mission VP4
- Mission VP5
- Mission VP6
- Mission VP7
- Mission VP8
- Mission VP9
- Mission WM1
- Mission WM2
- Mission WM3
- Mission WM4
- Mission WM5
- Mission WM6
- Mission WM7
- Mission WM8
- Mission WE1
- Mission WE10
- Mission WE2
- Mission WE3
- Mission WE4
- Mission WE5
- Mission WE6
- Mission WE7
- Mission WE8
- Mission WE9
- Vector Walk Interactive
- Name That Motion Interactive
- Kinematic Graphing 1 Concept Checker
- Kinematic Graphing 2 Concept Checker
- Graph That Motion Interactive
- Rocket Sled Concept Checker
- Force Concept Checker
- Free-Body Diagrams Concept Checker
- Free-Body Diagrams The Sequel Concept Checker
- Skydiving Concept Checker
- Elevator Ride Concept Checker
- Vector Addition Concept Checker
- Vector Walk in Two Dimensions Interactive
- Name That Vector Interactive
- River Boat Simulator Concept Checker
- Projectile Simulator 2 Concept Checker
- Projectile Simulator 3 Concept Checker
- Turd the Target 1 Interactive
- Turd the Target 2 Interactive
- Balance It Interactive
- Go For The Gold Interactive
- Egg Drop Concept Checker
- Fish Catch Concept Checker
- Exploding Carts Concept Checker
- Collision Carts - Inelastic Collisions Concept Checker
- Its All Uphill Concept Checker
- Stopping Distance Concept Checker
- Chart That Motion Interactive
- Roller Coaster Model Concept Checker
- Uniform Circular Motion Concept Checker
- Horizontal Circle Simulation Concept Checker
- Vertical Circle Simulation Concept Checker
- Race Track Concept Checker
- Gravitational Fields Concept Checker
- Orbital Motion Concept Checker
- Balance Beam Concept Checker
- Aluminum Can Polarization Concept Checker
- Charging Concept Checker
- Name That Charge Simulation
- Coulomb's Law Concept Checker
- Electric Field Lines Concept Checker
- Put the Charge in the Goal Concept Checker
- Circuit Builder Concept Checker (Series Circuits)
- Circuit Builder Concept Checker (Parallel Circuits)
- Circuit Builder Concept Checker (∆V-I-R)
- Circuit Builder Concept Checker (Voltage Drop)
- Equivalent Resistance Interactive
- Pendulum Motion Simulation Concept Checker
- Boundary Behavior Simulation Concept Checker
- Slinky Wave Simulator Concept Checker
- Simple Wave Simulator Concept Checker
- Wave Addition Simulation Concept Checker
- Standing Wave Maker Simulation Concept Checker
- Color Addition Concept Checker
- Painting With CMY Concept Checker
- Stage Lighting Concept Checker
- Filtering Away Concept Checker
- Young's Experiment Interactive
- Plane Mirror Images Interactive
- Who Can See Who Concept Checker
- Optics Bench (Mirrors) Concept Checker
- Name That Image (Mirrors) Interactive
- Refraction Concept Checker
- Total Internal Reflection Concept Checker
- Optics Bench (Lenses) Concept Checker
- Gaining Teacher Access
- 1-D Kinematics
- Newton's Laws
- Vectors - Motion and Forces in Two Dimensions
- Momentum and Its Conservation
- Work and Energy
- Circular Motion and Satellite Motion
- Thermal Physics
- Static Electricity
- Electric Circuits
- Vibrations and Waves
- Sound Waves and Music
- Light and Color
- Reflection and Mirrors
- About the Physics Interactives
- Task Tracker
- Usage Policy
- Newtons Laws
- Vectors and Projectiles
- Forces in 2D
- Momentum and Collisions
- Circular and Satellite Motion
- Balance and Rotation
- Waves and Sound
- 1-Dimensional Kinematics
- Circular, Satellite, and Rotational Motion
- Einstein's Theory of Special Relativity
- Waves, Sound and Light
- QuickTime Movies
- Forces in Two Dimensions
- Work, Energy, and Power
- Circular Motion and Gravitation
- Sound Waves
- About the Concept Builders
- Pricing For Schools
- Directions for Version 2
- Measurement and Units
- Relationships and Graphs
- Rotation and Balance
- Vibrational Motion
- Reflection and Refraction
- Teacher Accounts
- Task Tracker Directions
- Kinematic Concepts
- Kinematic Graphing
- Wave Motion
- Sound and Music
- About CalcPad
- 1D Kinematics
- Vectors and Forces in 2D
- Simple Harmonic Motion
- Rotational Kinematics
- Rotation and Torque
- Rotational Dynamics
- Light Waves
- Units and Measurement
- Stoichiometry
- Molarity and Solutions
- Thermal Chemistry
- Acids and Bases
- Kinetics and Equilibrium
- Solution Equilibria
- Newton's Laws of Motion
- Work and Energy Packet
- Static Electricity Review
- Graphing Practice
- About the ACT
- ACT Preparation
- For Teachers
- Other Resources
- Solutions Guide
- Solutions Guide Digital Download
- Motion in One Dimension
- Work, Energy and Power
- Purchasing the CD
- Purchasing the Digital Download
- About the NGSS Corner
- NGSS Search
- Force and Motion DCIs - High School
- Energy DCIs - High School
- Wave Applications DCIs - High School
- Force and Motion PEs - High School
- Energy PEs - High School
- Wave Applications PEs - High School
- Crosscutting Concepts
- The Practices
- Physics Topics
- NGSS Corner: Activity List
- NGSS Corner: Infographics
- About the Toolkits
- Position-Velocity-Acceleration
- Position-Time Graphs
- Velocity-Time Graphs
- Newton's First Law
- Newton's Second Law
- Newton's Third Law
- Terminal Velocity
- Projectile Motion
- Forces in 2 Dimensions
- Impulse and Momentum Change
- Momentum Conservation
- Work-Energy Fundamentals
- Work-Energy Relationship
- Circular Motion
- Roller Coaster Physics
- Satellite Motion
- Electric Fields
- Circuit Concepts
- Series Circuits
- Parallel Circuits
- Describing-Waves
- Wave Behavior Toolkit
- Standing Wave Patterns
- Resonating Air Columns
- Wave Model of Light
- Plane Mirrors
- Curved Mirrors
- Resource CD
- Teacher Guide
- Using Lab Notebooks
- Current Electricity
- Light Waves and Color
- Reflection and Ray Model of Light
- Refraction and Ray Model of Light
- Subscriptions
- Teacher Resources

- Newton's Laws
- Einstein's Theory of Special Relativity
- About Concept Checkers
- School Pricing
- Newton's Laws of Motion
- Newton's First Law
- Newton's Third Law
- Sample Problems and Solutions
- Kinematic Equations Introduction
- Solving Problems with Kinematic Equations
- Kinematic Equations and Free Fall
- Kinematic Equations and Kinematic Graphs

Check Your Understanding
Answer: d = 1720 m
Answer: a = 8.10 m/s/s
Answers: d = 33.1 m and v f = 25.5 m/s
Answers: a = 11.2 m/s/s and d = 79.8 m
Answer: t = 1.29 s
Answers: a = 243 m/s/s
Answer: a = 0.712 m/s/s
Answer: d = 704 m
Answer: d = 28.6 m
Answer: v i = 7.17 m/s
Answer: v i = 5.03 m/s and hang time = 1.03 s (except for in sports commericals)
Answer: a = 1.62*10 5 m/s/s
Answer: d = 48.0 m
Answer: t = 8.69 s
Answer: a = -1.08*10^6 m/s/s
Answer: d = -57.0 m (57.0 meters deep)
Answer: v i = 47.6 m/s
Answer: a = 2.86 m/s/s and t = 30. 8 s
Answer: a = 15.8 m/s/s
Answer: v i = 94.4 mi/hr
Solutions to Above Problems
d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s 2 )*(32.8 s) 2
Return to Problem 1
110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s) 2
110 m = (13.57 s 2 )*a
a = (110 m)/(13.57 s 2 )
a = 8.10 m/ s 2
Return to Problem 2
d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s 2 )*(2.60 s) 2
d = -33.1 m (- indicates direction)
v f = v i + a*t
v f = 0 + (-9.8 m/s 2 )*(2.60 s)
v f = -25.5 m/s (- indicates direction)
Return to Problem 3
a = (46.1 m/s - 18.5 m/s)/(2.47 s)
a = 11.2 m/s 2
d = v i *t + 0.5*a*t 2
d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s 2 )*(2.47 s) 2
d = 45.7 m + 34.1 m
(Note: the d can also be calculated using the equation v f 2 = v i 2 + 2*a*d)
Return to Problem 4
-1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s 2 )*(t) 2
-1.40 m = 0+ (-0.835 m/s 2 )*(t) 2
(-1.40 m)/(-0.835 m/s 2 ) = t 2
1.68 s 2 = t 2
Return to Problem 5
a = (444 m/s - 0 m/s)/(1.83 s)
a = 243 m/s 2
d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s 2 )*(1.83 s) 2
d = 0 m + 406 m
Return to Problem 6
(7.10 m/s) 2 = (0 m/s) 2 + 2*(a)*(35.4 m)
50.4 m 2 /s 2 = (0 m/s) 2 + (70.8 m)*a
(50.4 m 2 /s 2 )/(70.8 m) = a
a = 0.712 m/s 2
Return to Problem 7
(65 m/s) 2 = (0 m/s) 2 + 2*(3 m/s 2 )*d
4225 m 2 /s 2 = (0 m/s) 2 + (6 m/s 2 )*d
(4225 m 2 /s 2 )/(6 m/s 2 ) = d
Return to Problem 8
d = (22.4 m/s + 0 m/s)/2 *2.55 s
d = (11.2 m/s)*2.55 s
Return to Problem 9
(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(2.62 m)
0 m 2 /s 2 = v i 2 - 51.35 m 2 /s 2
51.35 m 2 /s 2 = v i 2
v i = 7.17 m/s
Return to Problem 10
(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(1.29 m)
0 m 2 /s 2 = v i 2 - 25.28 m 2 /s 2
25.28 m 2 /s 2 = v i 2
v i = 5.03 m/s
To find hang time, find the time to the peak and then double it.
0 m/s = 5.03 m/s + (-9.8 m/s 2 )*t up
-5.03 m/s = (-9.8 m/s 2 )*t up
(-5.03 m/s)/(-9.8 m/s 2 ) = t up
t up = 0.513 s
hang time = 1.03 s
Return to Problem 11
(521 m/s) 2 = (0 m/s) 2 + 2*(a)*(0.840 m)
271441 m 2 /s 2 = (0 m/s) 2 + (1.68 m)*a
(271441 m 2 /s 2 )/(1.68 m) = a
a = 1.62*10 5 m /s 2
Return to Problem 12
- (NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.)
First use: v f = v i + a*t
0 m/s = v i + (-9.8 m/s 2 )*(3.13 s)
0 m/s = v i - 30.7 m/s
v i = 30.7 m/s (30.674 m/s)
Now use: v f 2 = v i 2 + 2*a*d
(0 m/s) 2 = (30.7 m/s) 2 + 2*(-9.8 m/s 2 )*(d)
0 m 2 /s 2 = (940 m 2 /s 2 ) + (-19.6 m/s 2 )*d
-940 m 2 /s 2 = (-19.6 m/s 2 )*d
(-940 m 2 /s 2 )/(-19.6 m/s 2 ) = d
Return to Problem 13
-370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s 2 )*(t) 2
-370 m = 0+ (-4.9 m/s 2 )*(t) 2
(-370 m)/(-4.9 m/s 2 ) = t 2
75.5 s 2 = t 2
Return to Problem 14
(0 m/s) 2 = (367 m/s) 2 + 2*(a)*(0.0621 m)
0 m 2 /s 2 = (134689 m 2 /s 2 ) + (0.1242 m)*a
-134689 m 2 /s 2 = (0.1242 m)*a
(-134689 m 2 /s 2 )/(0.1242 m) = a
a = -1.08*10 6 m /s 2
(The - sign indicates that the bullet slowed down.)
Return to Problem 15
d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s 2 )*(3.41 s) 2
d = 0 m+ 0.5*(-9.8 m/s 2 )*(11.63 s 2 )
d = -57.0 m
(NOTE: the - sign indicates direction)
Return to Problem 16
(0 m/s) 2 = v i 2 + 2*(- 3.90 m/s 2 )*(290 m)
0 m 2 /s 2 = v i 2 - 2262 m 2 /s 2
2262 m 2 /s 2 = v i 2
v i = 47.6 m /s
Return to Problem 17
( 88.3 m/s) 2 = (0 m/s) 2 + 2*(a)*(1365 m)
7797 m 2 /s 2 = (0 m 2 /s 2 ) + (2730 m)*a
7797 m 2 /s 2 = (2730 m)*a
(7797 m 2 /s 2 )/(2730 m) = a
a = 2.86 m/s 2
88.3 m/s = 0 m/s + (2.86 m/s 2 )*t
(88.3 m/s)/(2.86 m/s 2 ) = t
t = 30. 8 s
Return to Problem 18
( 112 m/s) 2 = (0 m/s) 2 + 2*(a)*(398 m)
12544 m 2 /s 2 = 0 m 2 /s 2 + (796 m)*a
12544 m 2 /s 2 = (796 m)*a
(12544 m 2 /s 2 )/(796 m) = a
a = 15.8 m/s 2
Return to Problem 19
v f 2 = v i 2 + 2*a*d
(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(91.5 m)
0 m 2 /s 2 = v i 2 - 1793 m 2 /s 2
1793 m 2 /s 2 = v i 2
v i = 42.3 m/s
Now convert from m/s to mi/hr:
v i = 42.3 m/s * (2.23 mi/hr)/(1 m/s)
v i = 94.4 mi/hr
Return to Problem 20

IMAGES
VIDEO
COMMENTS
Physics problems with solutions and tutorials with full explanations are included. More emphasis on the topics of physics included in the SAT physics subject with hundreds of problems with detailed solutions. Physics concepts are clearly discussed and highlighted.
Express your answers to problems in this section to the correct number of significant figures and proper units. 11 . Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty.
HTML 5 apps designed for desktop, iPad and other tablets, are also included to explore interactively physics concepts. These apps "get" you closer to the physics concept you wish to understand. Practice Questions and Problems for Tests. Free Physics SAT and AP Practice Tests Questions. Physics Problems with Detailed Solutions and Explanations ...
You will need to get assistance from your school if you are having problems entering the answers into your online assignment. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.
See Answer See solution below. A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (assume a uniform acceleration). See Answer See solution below.