We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus AB : How to find position

Study concepts, example questions & explanations for AP Calculus AB

CREATE AN ACCOUNT Create Tests & Flashcards

Home Embed

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find Position

Given the velocity function $v(t)=t^3-t+7$ , find the position at time $x=2$ with initial position $x(0)=2$ .

Possible Answers:

Correct answer:

Explanation:

First, we find the position function $x(t)=\int (t^3-t+7) dt=\frac{t^4}{4}-\frac{t^2}{2}+7t+constant$

$x(0)=2\Rightarrow constant=2\Rightarrow x(t)=\frac{t^4}{4}-\frac{t^2}{2}+7t+2$

Therefore, $x(2)=\frac{2^4}{4}-\frac{2^2}{2}+7*2+2=18$ .

Report an Error

Example Question #1 : How To Find Position

Given the acceleration function is $a(t)=2t^2-t+3$ , intial velocity is 2 m/s, and the displacement at t=1 is x(1)=4 .

Find its initial position.

Possible Answers:

0.5

-0.5

Correct answer:

0.5

Explanation:

First, we find the velocity function by integrating the acceleration function $v(t)=\int 2t^2-t+3 = \frac{2}{3}t^3-\frac{1}{2}t^2+3t+c$

Since the initial velocity is 2 m/s, we have c=2 .

Then we integrate again to get the displacement function.

$x(t)=\int \frac{2}{3}t^3-\frac{1}{2}t^2+3t+2=\frac{1}{6}t^4-\frac{1}{6}t^3+\frac{3}{2}t^2+2t+k$

$x(1)=1.5+2+k=3.5+k=4$

This implies k=0.5

Report an Error

View AP Calculus AB Tutors

Frederick
Certified Tutor

Harvey Mudd College, Bachelor of Science, Mathematics. University of California-Berkeley, Master of Arts, Statistics.

View AP Calculus AB Tutors

David
Certified Tutor

Washington University in St Louis, Bachelors, Mathematics.

View AP Calculus AB Tutors

Therrin
Certified Tutor

The University of Tennessee, Bachelor of Science, Biochemistry and Molecular Biology.

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutoring in Boston, ACT Tutoring in New York City, GMAT Tutoring in Philadelphia, Biology Tutoring in Denver, SSAT Tutoring in Dallas Fort Worth, English Tutoring in Denver, Spanish Tutoring in Chicago, Biology Tutoring in Seattle, Computer Science Tutoring in Boston, Statistics Tutoring in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Chicago, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Philadelphia, Spanish Courses & Classes in New York City, Spanish Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in Washington DC, MCAT Test Prep in Denver, ACT Test Prep in Boston, SSAT Test Prep in Philadelphia, GRE Test Prep in Miami, SSAT Test Prep in Denver, LSAT Test Prep in Phoenix, SSAT Test Prep in Los Angeles, GMAT Test Prep in Atlanta, SAT Test Prep in Houston

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 Calculus AB : How to find position

Study concepts, example questions & explanations for AP Calculus AB

All AP Calculus AB Resources

Example Questions

Example Question #1 : How To Find Position

Example Question #1 : How To Find Position

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

FIND THE BEST TUTORS

Email address:
Your name:

Email address:
Your name:
Feedback: