We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Velocity

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

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 39 40 Next →

Example Question #71 : How To Find Velocity

The position equation of an object is given by the equation $x(t) = \cos^3(e^{4t})$ . What is the velocity of the object?

Possible Answers:

$v(t) = -3e^{4t}\cos(e^{4t})\sin(e^{4t})$

$v(t) = -12e^{4t}\cos^2(e^{4t})\sin(e^{4t})$

$v(t) = -3e^{4t}\cos^2(e^{4t})\sin(e^{4t})$

$v(t) = -12\cos^2(e^{4t})\sin(e^{4t})$

Correct answer:

$v(t) = -12e^{4t}\cos^2(e^{4t})\sin(e^{4t})$

Explanation:

The velocity of the object can be found by differentiating the object's position. This equation can be accurately differentiated using the chain rule and the power rule.

The chain rule is,

$f(x) = h(g(x)) \rightarrow f'(x) = h'(g(x) \times g'(x)$

and the power rule is,

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

Therefore the velocity of the object is

$v(t) = 3\cos^2(e^{4t})(-\sin(e^{4t}))(e^{4t})(4) = -12e^{4t}\cos^2(e^{4t})\sin(e^{4t})$ .

Report an Error

Example Question #72 : How To Find Velocity

A particles position, , as a function of time is given by

$s(t)=\frac{1}{2}a_1t^2+a_2t+a_3$

where a_1, a_2, a_3 are constants.

Find equations for the velocity, , and acceleration, , of the particle.

Possible Answers:

v=a_1t^2

a=a_1

v=a_2

a=a_3t

v=a_1t^2+a_2

a=0

v=a_1t+a_2

a=a_1

v=a_2t+a_3

a=0

Correct answer:

v=a_1t+a_2

a=a_1

Explanation:

The velocity of a moving object is given by $\frac{ds}{dt}$ .

The acceleration of a moving object is given by $\frac{d^2s}{dt^2}$ .

We will need to differntiate once to get velocity and another time to get the acceleration. We will need to use the power rule when differentiating. The power rule is as follows.

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

Using these formulas we find that

$v=\frac{1}{2}\cdot 2a_1t^{2-1}+a_2t^{1-1}=a_1t+a_2$

$a=a_1t^{1-1}=a_1$

Report an Error

Example Question #73 : How To Find Velocity

The position, , of a partice is given by the following equation.

s(t)=12t^3-6t^2-10

What is this particle's velocity at t=2 ?

Possible Answers:

112

104

120

Correct answer:

120

Explanation:

To find the velocity of the particle we first need to differentiate the position function. To take the derivative we will use the power rule.

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

Thus the velocity of a particle is found to be,

$v=\frac{ds}{dt}=36t^2-12t$ .

Plugging in for t=2, we find

v=120 .

Report an Error

Example Question #71 : How To Find Velocity

The position of an object is given by the equation $x(t) = \sin(e^{t^2})$ . What is the velocity of the object?

Possible Answers:

$v(t) = -2t\cos(e^{t^2})$

$v(t) = 2t\cos(e^{t^2})$

$v(t) = 2\cos(e^{t^2})$

$v(t) = 2te^{t^2}\cos(e^{t^2})$

Correct answer:

$v(t) = 2te^{t^2}\cos(e^{t^2})$

Explanation:

The velocity of the object can be found by differentiating the position of the object. To accurately differentiate the position we can use the power rule and the chain rule.

The power rule is, $f(x) = x^n \rightarrow f'(x) = nx^{n-1}$ .

The chain rule is, $f(x) = h(g(x)) \rightarrow f'(x) = h'(g(x) \times g'(x)$ .

Differenting the object's position using these two equations gives

$v(t) = \cos(e^{t^2})(e^{t^2})((2)t^{(2-1)}) = 2te^{t^2}\cos(e^{t^2})$ .

Report an Error

Example Question #75 : How To Find Velocity

The position of an object is given by the equation $x(t) = 10t^2\sin(t)$ . What is the velocity of the object?

Possible Answers:

$v(t) = 20t\sin(t) - 10t^2\cos(t)$

$v(t) = 20t\sin^2(t) - 10t^2\cos(t)$

$v(t) = 20t\sin(t) + 10t^2\cos(t)$

$v(t) = 20t\sin(t) - 10t\cos(t)$

Correct answer:

$v(t) = 20t\sin(t) + 10t^2\cos(t)$

Explanation:

The velocity of the object can be found by differentiating the object's position. To accurately differentiate the object's position we can use the product rule and the power rule where if

$f(x)= j(x)k(x) \rightarrow f'(x) = j'(x)k(x) + j(x)k'(x)$

and if

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

Using these rules the velocity equation is

$v(t) = 10(2)t^{(2-1)}\sin(t) + 10t^2\cos(t) = 20t\sin(t) + 10t^2\cos(t)$ .

Report an Error

Example Question #76 : How To Find Velocity

The position of an object is given by the equation $x(t) = \cos^4(t)$ . What is the velocity of the object at t = 2 ?

Possible Answers:

$a(t) = -\cos^4(2)\sin(2)$

$a(t) = 4\cos^3(2)\sin(2)$

$a(t) = -4\cos^3(2)\sin(2)$

$a(t) = 2\cos^3(2)\sin(2)$

Correct answer:

$a(t) = -4\cos^3(2)\sin(2)$

Explanation:

The velocity of the object is equal to the derivative of the object's position. The velocity can be found using the power rule and the chain rule where if $f(x) = x^n \rightarrow f'(x) = nx^{n-1}$

and if

$f(x) = h(g(x)) \rightarrow f'(x) = h'(g(x) \times g'(x)$ .

Therefore the velocity of the object is

$a(t) =(4)\cos^{(4-1)}(t)(-\sin(t)) = -4\cos^3(t)\sin(t)$ .

At time t =2 , the velocity is

$a(t) = -4\cos^3(2)\sin(2)$ .

Report an Error

Example Question #77 : How To Find Velocity

The acceleration of an object is given by the equation $a(t) = \frac{-2}{t^3}$ . What is the velocity of the object at time t=1 , if the initial velocity of the object is ?

Possible Answers:

None of the above.

Correct answer:

Explanation:

The velocity of the object can be found by integrating the acceleration. This can be done using the power rule where if

$f'(x) = x^n \rightarrow f(x) = \frac{x^{n+1}}{n+1}$ .

Using this rule the velocity of the object is

$v(t) = \int (\frac{-2}{t^3})dt = \int (-2t^{-3})dt = \frac{-2t^{(-3+1)}}{-3+1} +C = t^{-2} +C$ .

The constant can be found using the initial velocity of the object.

$v(0) = (0)^{-2}+ C = 0 +C = 2$

Therefore C = 2 and $v(t) = t^{-2} + 2$ .

With the velocity equation we solve for the velocity at t= 1 .

$v(1) = (1)^{-2} + 2 = 1 + 2 = 3$

Report an Error

Example Question #78 : How To Find Velocity

The position equation of an object is $x(t) = t^2\sin(t)$ . What is the velocity of the object?

Possible Answers:

$v(t) = 2\sin(t) - t^2\cos(t)$

$v(t) = 2t\sin(t) + t^2\cos(t)$

$v(t) = 2t\sin(t) - t^2\cos(t)$

$v(t) = 2t\sin(t)\cos(t)$

Correct answer:

$v(t) = 2t\sin(t) + t^2\cos(t)$

Explanation:

To find the velocity we can differentiate the position of the object. To do this accurately we use the product rule and the power rule.

The product rule is

$f(x)= j(x)k(x) \rightarrow f'(x) = j'(x)k(x) + j(x)k'(x)$ .

The power rule is

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

The velocity of the equation is then found to be

$v(t) = (2)t^{(2-1)}\sin(t) + t^2(\cos(t)) = 2t\sin(t) + t^2\cos(t)$ .

Report an Error

Example Question #79 : How To Find Velocity

The position of an object is given by the equation x(t) = 4t^2 . What is the velocity of the object at time t =10 ?

Possible Answers:

400

1333

Correct answer:

Explanation:

The velocity of the object is equal to the derivative of the position. To differentiate the position we use the power rule where if

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

With this rule we find the velocity equation to be

$v(t) = x'(t) = 4(2)t^{(2-1)} = 8t$ .

Using time t = 10 , we can obtain a velocity of

v(10) = 8(10) = 80 .

Report an Error

Example Question #80 : How To Find Velocity

The acceleration of an object is given by the equation a(t) = 12 . What is the velocity of the object, if the initial velocity of the object is ?

Possible Answers:

v(t) = 6t^2

v(t) = 12t

v(t) = 2t^3

v(t) = 12t - 12

Correct answer:

v(t) = 12t

Explanation:

To find the velocity we must integrate the acceleration using the power rule.

The power rule is where

$f'(x) = x^n \rightarrow f(x) = \frac{x^{n+1}}{n+1}$ .

Applying this to the acceleration equation gives

$v(t) = \int (12t^0)dt = \frac{12t^{(0+1)}}{0+1} + C = 12t +C$ .

Using the initial velocity we find the value of .

v(0) = 12(0) + C = 0 + C = 0

Therefore C = 0 and v(t) = 12t .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 39 40 Next →

View Calculus Tutors

Heather
Certified Tutor

University of Wisconsin-River Falls, Bachelor of Science, Mathematics. University of Iowa, Master of Science, Mathematics.

View Calculus Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

View Calculus Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

All Calculus 1 Resources

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

Popular Subjects

LSAT Tutors in Atlanta, Biology Tutors in Washington DC, ACT Tutors in Miami, SSAT Tutors in San Francisco-Bay Area, ACT Tutors in Washington DC, Spanish Tutors in Houston, SAT Tutors in Phoenix, Math Tutors in Denver, Math Tutors in Phoenix, Math Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in San Diego, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Denver, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Houston, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in New York City, GRE Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in San Diego, ACT Test Prep in Denver, ISEE Test Prep in Houston, ISEE Test Prep in Los Angeles, GMAT Test Prep in San Diego, ACT Test Prep in Washington DC, ISEE Test Prep in Philadelphia, GMAT Test Prep in Atlanta, ACT Test Prep in Boston, MCAT Test Prep in Philadelphia

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 : Velocity

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #71 : How To Find Velocity

Example Question #72 : How To Find Velocity

Example Question #73 : How To Find Velocity

Example Question #71 : How To Find Velocity

Example Question #75 : How To Find Velocity

Example Question #76 : How To Find Velocity

Example Question #77 : How To Find Velocity

Example Question #78 : How To Find Velocity

Example Question #79 : How To Find Velocity

Example Question #80 : How To Find Velocity

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: