Call Now to Set Up Tutoring:

(888) 888-0446

AP Physics C: Mechanics : Kinetic Energy

Study concepts, example questions & explanations for AP Physics C: Mechanics

Create An Account

All AP Physics C: Mechanics Resources

2 Diagnostic Tests 92 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Energy

A train car with a mass of 2400 kg starts from rest at the top of a 150 meter-high hill. What will its velocity be when it reaches the bottom of the hill, assuming that the bottom of the hill is the reference level.

Possible Answers:

$51.65 \frac{m}{s}$ $\displaystyle 51.65 \frac{m}{s}$

$55.0 \frac{m}{s^2}$ $\displaystyle 55.0 \frac{m}{s^2}$

$51.65 \frac{m}{s^2}$ $\displaystyle 51.65 \frac{m}{s^2}$

$0 \frac{m}{s}$ $\displaystyle 0 \frac{m}{s}$

$54.25 \frac{m}{s}$ $\displaystyle 54.25 \frac{m}{s}$

Correct answer:

$54.25 \frac{m}{s}$ $\displaystyle 54.25 \frac{m}{s}$

Explanation:

The law of conservation of energy states:

$\displaystyle PE_i + KE_i = PE_f + KE_f$

If the car starts at rest, then the initial kinetic energy = 0 J.

If the car ends at the reference height, the final potential energy = 0 J.

Subsituting these values, the equation becomes:

$\displaystyle PE_i + 0 J = 0 J + KE_f$

The initial potential energy can be determined by:

$PE_i = mgh_i \\ PE_i = 2400 kg \cdot 9.81 \frac{m}{s^2} \cdot 150 m\\ PE_i = 3531600 \frac{kg \cdot m^2}{s^2}\\ PE_i = 3531600 J$ $\displaystyle PE_i = mgh_i \\ PE_i = 2400 kg \cdot 9.81 \frac{m}{s^2} \cdot 150 m\\ PE_i = 3531600 \frac{kg \cdot m^2}{s^2}\\ PE_i = 3531600 J$

The final kinetic energy equation is:

$KE_f = \frac{1}{2}mv_f^2\\ KE_f = \frac{1}{2}(2400 kg)v_f^2$ $\displaystyle KE_f = \frac{1}{2}mv_f^2\\ KE_f = \frac{1}{2}(2400 kg)v_f^2$

Substituting the initial potential energy and final kinetic energy into our modified conservation of energy equation, we get:

$3531600 J = \frac{1}{2}(2400 kg)v_f^2\\ 3531600 \frac{kg\cdot m^2}{s^2} = 1200 kg \cdot v_f^2\\ \frac{3531600 \frac{kg\cdot m^2}{s^2}}{1200 kg}=v_f^2\\ 2943 \frac{m^2}{s^2}=v_f^2\\ \sqrt{2943 \frac{m^2}{s^2}}=\sqrt{v_f^2}\\ 54.25 \frac{m}{s}=v_f$ $\displaystyle 3531600 J = \frac{1}{2}(2400 kg)v_f^2\\ 3531600 \frac{kg\cdot m^2}{s^2} = 1200 kg \cdot v_f^2\\ \frac{3531600 \frac{kg\cdot m^2}{s^2}}{1200 kg}=v_f^2\\ 2943 \frac{m^2}{s^2}=v_f^2\\ \sqrt{2943 \frac{m^2}{s^2}}=\sqrt{v_f^2}\\ 54.25 \frac{m}{s}=v_f$

Report an Error

Example Question #21 : Work, Energy, And Power

An object has a mass of 5kg and has a position described by the given function:

$\displaystyle x(t)=2x^2-5x+12$

What is the object's kinetic energy after two seconds?

Possible Answers:

22.5J $\displaystyle 22.5J$

7.5J $\displaystyle 7.5J$

27.5J $\displaystyle 27.5J$

45.2J $\displaystyle 45.2J$

Correct answer:

22.5J $\displaystyle 22.5J$

Explanation:

Kinetic energy is defined by the equation:

$KE=\frac{1}{2}mv^2$ $\displaystyle KE=\frac{1}{2}mv^2$

Taking the derivative of the position function allows us to obtain the velocity function:

$\displaystyle x'(t)=v(t)=4x-5$

We can now determine the velocity after two seconds:

$\displaystyle v(2)=4(2)-5=3$

Now that we know our velocity, we can solve for the kinetic energy.

$KE=\frac{1}{2}(5kg)(3\frac{m}{s})^2=22.5J$ $\displaystyle KE=\frac{1}{2}(5kg)(3\frac{m}{s})^2=22.5J$

Report an Error

Example Question #22 : Work, Energy, And Power

An object starts from rest and accelerates at a rate of $2.5\frac{m}{s^2}$ $\displaystyle 2.5\frac{m}{s^2}$. If the object has a mass of 10kg, what is its kinetic energy after three seconds?

Possible Answers:

281.25J $\displaystyle 281.25J$

226.5J $\displaystyle 226.5J$

75J $\displaystyle 75J$

562.64J $\displaystyle 562.64J$

Correct answer:

281.25J $\displaystyle 281.25J$

Explanation:

Kinetic energy is given by the equation:

$KE=\frac{1}{2}mv^2$ $\displaystyle KE=\frac{1}{2}mv^2$

We can find the velocity using the given acceleration and time:

$v=v_o+a\Delta t$ $\displaystyle v=v_o+a\Delta t$

$v=0\frac{m}{s}+(2.5\frac{m}{s^2})(3s)=7.5\frac{m}{s}$ $\displaystyle v=0\frac{m}{s}+(2.5\frac{m}{s^2})(3s)=7.5\frac{m}{s}$

Use this velocity to find the kinetic energy after three seconds:

$KE=\frac{1}{2}(10kg)(7.5\frac{m}{s})^2=281.25J$ $\displaystyle KE=\frac{1}{2}(10kg)(7.5\frac{m}{s})^2=281.25J$

Report an Error

Example Question #23 : Work, Energy, And Power

A 120kg box has a kinetic energy of 2300J. What is its velocity?

Possible Answers:

$7.2\frac{m}{s}$ $\displaystyle 7.2\frac{m}{s}$

$38.3\frac{m}{s}$ $\displaystyle 38.3\frac{m}{s}$

$40.1\frac{m}{s}$ $\displaystyle 40.1\frac{m}{s}$

$6.2\frac{m}{s}$ $\displaystyle 6.2\frac{m}{s}$

$19.4\frac{m}{s}$ $\displaystyle 19.4\frac{m}{s}$

Correct answer:

$6.2\frac{m}{s}$ $\displaystyle 6.2\frac{m}{s}$

Explanation:

The formula for kinetic energy of an object is:

$KE=\frac{1}{2}mv^2$ $\displaystyle KE=\frac{1}{2}mv^2$

The problem gives us the mass and the kinetic energy, and asks for the velocity, so we can rearrange the equation:

$v=\sqrt{\frac{2KE}{m}}$ $\displaystyle v=\sqrt{\frac{2KE}{m}}$

Use our given values for kinetic energy and mass to solve:

$v=\sqrt{\frac{2(2300J)}{120kg}}=6.2\frac{m}{s}$ $\displaystyle v=\sqrt{\frac{2(2300J)}{120kg}}=6.2\frac{m}{s}$

Report an Error

View Tutors

Brian
Certified Tutor

New York University, Masters in Business Administration, Business, General.

View Tutors

Godfrey
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Chemistry. CUNY Queens College, Master of Science, Environmental Science.

View Tutors

Cynthia
Certified Tutor

Arizona State University, Bachelors, Psychology. Arizona State University, Master in Public Health, Psychology.

All AP Physics C: Mechanics Resources

2 Diagnostic Tests 92 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Dallas Fort Worth, Reading Tutors in Dallas Fort Worth, Computer Science Tutors in New York City, Algebra Tutors in Boston, Chemistry Tutors in Chicago, LSAT Tutors in Chicago, Computer Science Tutors in Boston, Math Tutors in Houston, Chemistry Tutors in Dallas Fort Worth, MCAT Tutors in Washington DC

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Washington DC, GMAT Courses & Classes in Boston, SAT Courses & Classes in San Diego, Spanish Courses & Classes in Phoenix, SAT Courses & Classes in Phoenix, ACT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Chicago, SSAT Courses & Classes in Seattle

Popular Test Prep

LSAT Test Prep in Philadelphia, ACT Test Prep in Seattle, ISEE Test Prep in Denver, SSAT Test Prep in Atlanta, ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Chicago, LSAT Test Prep in Seattle, SSAT Test Prep in Houston, GMAT Test Prep in San Diego

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

AP Physics C: Mechanics : Kinetic Energy

Study concepts, example questions & explanations for AP Physics C: Mechanics

All AP Physics C: Mechanics Resources

Example Questions

Example Question #3 : Energy

Example Question #21 : Work, Energy, And Power

Example Question #22 : Work, Energy, And Power

Example Question #23 : Work, Energy, And Power

All AP Physics C: Mechanics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: