Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : How to find acceleration

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Acceleration

A car is moving at a constant speed of miles per hour. What is the acceleration after hours?

Possible Answers:

Correct answer:

Explanation:

The car is moving at a constant speed of 40 miles per hour, so the velocity function is:

v(t)=40

The derivative of the velocity function is the acceleration function.

a(t)=0

The acceleration at any particular time is zero.

Report an Error

Example Question #12 : Acceleration

The position of an object, in meters, is given by the following equation:

$s(t)=4t^2-\frac{11}{3}t-7$

Find the acceleration of the object.

Possible Answers:

m/s^2

9.8 m/s^2

3.2 m/s^2

m/s^2

Correct answer:

m/s^2

Explanation:

Velocity is the derivative of position, and acceleration is the derivative of velocity, so acceleration is the second derivative of position. With that in mind, all we have to do to find the acceleration of the object is take the derivative of the equation for its position twice.

$s(t)=4t^2-\frac{11}{3}t-7$

$v(t)=s'(t)=8t-\frac{11}{3}$

a(t)=v'(t)=s''(t)=8

Report an Error

Example Question #13 : Acceleration

The velocity of an object is given by the following equation:

$v(t)=\frac{3}{2}t^2-\frac{1}{3}t+16$

Find the equation for the acceleration of the object.

Possible Answers:

$a(t)=\frac{1}{3}t-3$

$a(t)=\frac{1}{2}t-16$

$a(t)=3t-\frac{1}{3}$

$a(t)=16t+\frac{1}{3}$

a(t)=2t+16

Correct answer:

$a(t)=3t-\frac{1}{3}$

Explanation:

Acceleration is the derivative of velocity, so in order to find the equation for the object's acceleration, we must take the derivative of the equation for its velocity:

$v(t)=\frac{3}{2}t^2-\frac{1}{3}t+16$

We will use the power rule to find the derivative which states:

$f(x)=ax^n \rightarrow f'(x)=a\cdot nx^{n-1}$

$a(t)=v'(t)=\frac{3}{2}\cdot 2t^1-\frac{1}{3}t^0=3t-\frac{1}{3}$

Report an Error

Example Question #14 : Acceleration

The acceleration of an object is given by the folowing indefinite integral:

$a(t)=\int \left(\frac{1}{5}t-\frac{1}{10}\right)dt$

If a(0)=0.1 , find the acceleration of the object at t=3 seconds.

Possible Answers:

0.7 m/s^2

0.3 m/s^2

0.1 m/s^2

m/s^2

Correct answer:

0.7 m/s^2

Explanation:

In order to find a(3), our first step is to evaluate the integral in the equation for acceleration:

$a(t)=\int \left(\frac{1}{5}t-\frac{1}{10}\right)dt=\frac{1}{10}t^2-\frac{1}{10}t+C$

Now we use the initial acceleration, a(0)=0.1, to solve for the constant C:

$a(t)=\frac{1}{10}t^2-\frac{1}{10}t+C\rightarrow a(0)=0+0+C=0.1\rightarrow C=0.1$

So if C=0.1, then our final equation for acceleration is as follows, which we can then plug t=3 into to find the acceleration of the object after 3 seconds, a(3):

$a(t)=\frac{1}{10}t^2-\frac{1}{10}t+0.1$

$a(3)=\frac{1}{10}(3)^2-\frac{1}{10}(3)+0.1=0.9-0.3+0.1=0.7$

Report an Error

Example Question #11 : Acceleration

The position of an object is described by the following equation:

$s(t)=\frac{5}{4}t^3-3t^2+\frac{1}{2}t-6$

Find the acceleration of the object at t=1 second.

Possible Answers:

$\frac{15}{2}$ m/s^2

m/s^2

$\frac{5}{4}$ m/s^2

$\frac{3}{2}$ m/s^2

m/s^2

Correct answer:

$\frac{3}{2}$ m/s^2

Explanation:

Acceleration is the second derivative of position, so we must first find the second derivative of the equation for position:

$s(t)=\frac{5}{4}t^3-3t^2+\frac{1}{2}t-6$

$v(t)=s'(t)=\frac{15}{4}t^2-6t+\frac{1}{2}$

$a(t)=v'(t)=s''(t)=\frac{15}{2}t-6$

Now we can plug in t=1 to find the acceleration of the object after 1 second:

$a(1)=\frac{15}{2}(1)-6=\frac{3}{2}$

Report an Error

Example Question #14 : Acceleration

The velocity of an object is given by the following equation:

$v(t)=\frac{3}{7}t^2-\frac{1}{14}t+5$

Find the acceleration of the object at t=2 seconds.

Possible Answers:

m/s^2

$\frac{23}{14}$ m/s^2

$\frac{3}{7}$ m/s^2

$\frac{1}{14}$ m/s^2

$\frac{6}{7}$ m/s^2

Correct answer:

$\frac{23}{14}$ m/s^2

Explanation:

Acceleration is the derivative of velocity, so we must take the derivative of the given equation to find an equation for acceleration:

$v(t)=\frac{3}{7}t^2-\frac{1}{14}t+5$

$a(t)=v'(t)=\frac{6}{7}t-\frac{1}{14}$

Now we can plug in t=2 to find the acceleration of the object at 2 seconds:

$a(2)=\frac{6}{7}(2)-\frac{1}{14}=\frac{12}{7}-\frac{1}{14}=\frac{24}{14}-\frac{1}{14}=\frac{23}{14}$

Report an Error

Example Question #15 : Acceleration

The position vector of an object moving in a plane is given by r(t) = t^4i+3t^2j . Find the object's acceleration when t=3 .

Possible Answers:

102ij

108i+6j

114

114ij

Correct answer:

108i+6j

Explanation:

To find the acceleration, we must differentiate the position vector twice. Differentiating the position vector once gives the velocity vector:

$v(t) = (1\cdot 4)t^{4-1}i+(3\cdot 2)t^{2-1}j = 4t^3i+6tj$

Differentiating the second time gives acceleration:

$a(t) = (4\cdot 3)t^{3-1}i+(6\cdot 1)t^{1-1}j = 12t^2i+6j$

Using 3 as the value for gives

$a(3) = 12(3)^2i+6j = 12\cdot 9i + 6j = 108i+6j$

Report an Error

Example Question #16 : Acceleration

If the position of a particle is: s(t) = 3t^3 + 10t , What is the acceleration at t = 3 ?

Possible Answers:

Correct answer:

Explanation:

To find the acceleration equation of the particle, we can differentiate the position equation twice.

Differentiating once gives the velocity equation:

v(t) = 9t^2+10

Differentiating again give the acceleration equation:

a(t) = 18t

Using 3 as the value for ,

a(3) = 18(3) = 54

Report an Error

Example Question #17 : Acceleration

What is the acceleration at time t=4secs when the acceleration is given by a(t)=4t . is time in seconds.

Possible Answers:

a(4)=16

a(4)=12

a(4)=8

a(4)=4

a(4)=18

Correct answer:

a(4)=16

Explanation:

To find the acceleration at time 4 seconds, we simply subsitute in 4 seconds into the acceleration function.

$a(4)=4\cdot 4$

a(4)=16

Report an Error

Example Question #15 : Acceleration

The velocity function is v(t)=4t .

What is the acceleration function?

Possible Answers:

a(t)=4t

a(t)=2

a(t)=4

a(t)=4t^2

a(t)=2t^2

Correct answer:

a(t)=4

Explanation:

To find the acceleration function we take the derivative of the velocity function

So v(t)=4t will turn into:

a(t)=4

because of Power Rule,

$p(t)=a^n \rightarrow v(t)=na^{n-1}$

$v(t)=4\cdot 1 t^{1-1}=4t^0=4(1)=4$ .

Report an Error

View Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Calculus Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Calculus Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Chicago, Statistics Tutors in Denver, GRE Tutors in Seattle, Biology Tutors in Houston, MCAT Tutors in Atlanta, SSAT Tutors in Boston, Computer Science Tutors in Philadelphia, Reading Tutors in Atlanta, MCAT Tutors in San Francisco-Bay Area, ISEE Tutors in Atlanta

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Atlanta, ACT Courses & Classes in Houston, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in New York City

Popular Test Prep

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

Calculus 1 : How to find acceleration

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #11 : Acceleration

Example Question #12 : Acceleration

Example Question #13 : Acceleration

Example Question #14 : Acceleration

Example Question #11 : Acceleration

Example Question #14 : Acceleration

Example Question #15 : Acceleration

Example Question #16 : Acceleration

Example Question #17 : Acceleration

Example Question #15 : Acceleration

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: