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

Example Question #371 : How To Find Velocity

The velocity function of a particle and a position of this particle at a known time are given by v(t)=t^4+sin(t) p(0)=3 . Approximate $p(\pi)$ using Euler's Method and three steps.

Possible Answers:

2.934

5.166

26.222

33.288

41.950

Correct answer:

26.222

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=t^4+sin(t) p(0)=3

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{\pi-0}{3}=\frac{\pi}{3}$

p_0=3;t_0=0

$p_1=3+(\frac{\pi}{3})(0^4+sin(0))=3$

$p_2=3+(\frac{\pi}{3})((\frac{\pi}{3})^4+sin(\frac{\pi}{3}))=5.166$

$p_3=5.166+(\frac{\pi}{3})((\frac{2\pi}{3})^4+sin(\frac{2\pi}{3}))=26.222$

Report an Error

Example Question #372 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=ln(t^3) p(10)=0 . Approximate p(1000) using Euler's Method and three steps.

Possible Answers:

12340.9

8020.7

23017.1

5508.2

14492.5

Correct answer:

14492.5

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=ln(t^3) p(10)=0

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{1000-10}{3}=330$

p_0=0;t_0=10

p_1=0+(330)ln(10^3)=2279.6

p_2=2279.6+(330)ln(340^3)=8050.3

p_3=8050.3+(330)ln(670^3)=14492.5

Report an Error

Example Question #372 : How To Find Velocity

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=te^{t}cos(t)$ p(0)=0 . Approximate p(1) using Euler's Method and two steps

Possible Answers:

1.096

0.183

0.734

0.362

Correct answer:

0.362

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told $v(t)=te^{t}cos(t)$ p(0)=0

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{1-0}{2}=0.5$

p_0=0;t_0=0

$p_1=0+(0.5)(0)e^{0}cos(0)=0$

$p_2=0+(0.5)(0.5)e^{0.5}cos(0.5)=0.362$

Report an Error

Example Question #374 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=(t-7)^3 p(6)=0 . Approximate p(7) using Euler's Method and two steps

Possible Answers:

-0.563

-0.5

0.5

-0.063

Correct answer:

-0.563

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=(t-7)^3 p(6)=0

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{7-6}{2}=0.5$

p_0=0;t_0=6

p_1=0+(0.5)(6-7)^3=-0.5

p_2=-0.5+(0.5)(6.5-7)^3=-0.563

Report an Error

Example Question #375 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=4t^2+3t+1 p(0)=0 . Approximate p(2) using Euler's Method and two steps.

Possible Answers:

$\frac{56}{3}$

Correct answer:

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=4t^2+3t+1 p(0)=0

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{2-0}{2}=1$

p_0=0;t_0=0

p_1=0+(1)(4(0)^2+3(0)+1)=1

p_2=1+(1)(4(1)^2+3(1)+1)=9

Report an Error

Example Question #376 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=4sin^2(t) and $p(\frac{\pi}{2})=1$ . Approximate $p(\pi)$ using Euler's Method and two steps.

Possible Answers:

4.142

5.713

2.089

6.552

1.726

Correct answer:

5.713

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=4sin^2(t) and $p(\frac{\pi}{2})=1$

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{\pi-\frac{\pi}{2}}{2}=\frac{\pi}{4}$

$p_0=1;t_0=\frac{\pi}{2}$

$p_1=1+(\frac{\pi}{4})(4sin^2(\frac{\pi}{2}))=4.142$

$p_2=4.142+(\frac{\pi}{4})(4sin^2(\frac{3\pi}{4}))=5.713$

Report an Error

Example Question #377 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=tan^2(t^2) and p(0)=4 . Approximate $p(0.5\pi)$ using Euler's Method and two steps.

Possible Answers:

4.126

1.395

4.395

5.261

1.261

Correct answer:

4.395

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=tan^2(t^2) and p(0)=4

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{0.5\pi-0}{2}=0.25\pi$

p_0=4;t_0=0

$p_1=4+(0.25\pi)(tan^2(0^2))=4$

$p_2=4+(0.25\pi)(tan^2((0.25\pi)^2))=4.395$

Report an Error

Example Question #378 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=cos^3(t) and p(0)=7 . Approximate $p(\pi)$ using Euler's Method and two steps.

Possible Answers:

2.316

1.571

8.571

9.316

Correct answer:

8.571

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=cos^3(t) and p(0)=7

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{\pi-0}{2}=\frac{\pi}{2}$

p_0=7;t_0=0

$p_1=7+(\frac{\pi}{2})cos^3(0)=8.571$

$p_2=8.571+(\frac{\pi}{2})cos^3(\frac{\pi}{2})=8.571$

Report an Error

Example Question #379 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by v(t)=ln(cos(t^3)) and p(0)=1 . Approximate p(8) using Euler's Method and two steps.

Possible Answers:

-0.75

4.75

3.75

-2.75

Correct answer:

-2.75

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told v(t)=ln(cos(t^3)) and p(0)=1

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{8-0}{2}=4$

p_0=1;t_0=0

p_1=1+(4)ln(cos(0^3))=1

p_2=1+(4)ln(cos(4^3))=-2.75

Report an Error

Example Question #380 : Calculus

The velocity function of a particle and a position of this particle at a known time are given by $v(t)=e^{\frac{t^2}{4}}$ and p(1)=3 . Approximate p(3) using Euler's Method and two steps.

Possible Answers:

8.432

7.002

4.284

5.718

Correct answer:

7.002

Explanation:

The general form of Euler's method, when a derivative function, initial value, and step size are known, is:

$y_n=y_{n+1} +\Delta x f'(x_n,y_n)$

In the case of this problem, this can be rewritten as:

$p(t_n)=p(t_{n+1}) +\Delta t v(t_n)$

To calculate the step size find the difference between the final and initial value of and divide by the number of steps to be used:

$\Delta t = \frac{t_f-t_i}{Steps}$

For this problem, we are told $v(t)=e^{\frac{t^2}{4}}$ and p(1)=3

Knowing this, we may take the steps to estimate our function value at our desired value:

$\Delta t = \frac{3-1}{2}=1$

p_0=3;t_0=1

$p_1=3+(1)e^{\frac{1^2}{4}}=4.284$

$p_2=4.284+(1)e^{\frac{2^2}{4}}=7.002$

Report an Error

View Calculus Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

View Calculus Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Calculus Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

All Calculus 1 Resources

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

Popular Subjects

Calculus Tutors in Seattle, French Tutors in New York City, ISEE Tutors in San Francisco-Bay Area, English Tutors in Philadelphia, MCAT Tutors in Phoenix, MCAT Tutors in Houston, English Tutors in Denver, Math Tutors in Houston, Reading Tutors in New York City, SSAT Tutors in Los Angeles

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Phoenix, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Chicago, SAT Courses & Classes in Boston, Spanish Courses & Classes in Boston, SSAT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Boston, GMAT Test Prep in Houston, LSAT Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Houston, MCAT Test Prep in Chicago, SAT Test Prep in Philadelphia, ISEE Test Prep in Atlanta, ACT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth

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 #371 : How To Find Velocity

Example Question #372 : Calculus

Example Question #372 : How To Find Velocity

Example Question #374 : Calculus

Example Question #375 : Calculus

Example Question #376 : Calculus

Example Question #377 : Calculus

Example Question #378 : Calculus

Example Question #379 : Calculus

Example Question #380 : Calculus

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: