We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : How to find position

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 #6 : Integration

The velocity of an object is v(t) = 3t^2 . What is the position of the object if its initial position is 1000 ?

Possible Answers:

x(t) = 6t +1000

x(t) = t^3 +1000

$x(t) = \frac{t^4}{4} +1000$

x(t) = t^3 -1000

Correct answer:

x(t) = t^3 +1000

Explanation:

The position is the integral of the velocity. By integrating with the power rule we can find the object's position.

The power rule is where

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

Therefore the position of the object is

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

We can solve for the constant using the object's initial position.

x(0) = (0)^3 + C = 0+C =1000

Therefore C= 1000 and x(t) = t^3 +1000 .

Report an Error

Example Question #32 : How To Find Position

The velocity of an object is given by the equation v(t) = 18t^2 - 11 . What is the position of the object at time t= 3 if the initial position of the object is ?

Possible Answers:

139

Correct answer:

139

Explanation:

The position of the object can be found by integrating the velocity. 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 we find that

$x(t) = \int (18t^2-11)dt = \frac{18t^{(2+1)}}{2+1} - \frac{11t^{(0+1)}}{0+1} +C = 6t^3 - 11t +C$ .

We can find the value of using the initial position of the object.

x(0) = 6(0)^3 - 11(0) +C = 0 - 0 +C =10

Therefore C = 10 and x(t) = 6t^3 - 11t +10 .

x(3) = 6(3)^3 - 11(3) + 10 = 162 - 11(3) + 10 = 139

Report an Error

Example Question #33 : How To Find Position

The velocity of an object is given by the equation v(t) = 44t^3 + t^2 +2 . What is the position of the object at time t =1 , if the initial position of the object is ?

Possible Answers:

$9 \frac{1}{3}$

$15 \frac{1}{3}$

$11 \frac{1}{3}$

Correct answer:

$15 \frac{1}{3}$

Explanation:

The position of the object can be found by integrating the velocity. 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 to integrate the velocity gives us

$x(t) = \int (44t^3 + t^2 + 2)dt = \frac{44t^{(3+1)}}{3+1} + \frac{t^{(2+1)}}{2+1} +\frac{2t^{(0+1)}}{0+1} +C$

$x(t) = 11t^4 + \frac{t^3}{3} + 2t +C$ .

The value of can be found by using the initial position of the object.

$x(0)= 11(0)^4 +\frac{(0)^3}{3} + 2(0) +C = 0 + 0+0+C = 2$

Therefore C = 2 and $x(t) = 11t^4 + \frac{t^3}{3} + 2t + 2$ .

Using the position equation we find the position at t = 1 .

$x(1) = 11(1)^4 + \frac{(1)^3}{3} + 2(1) +2 = 11 + \frac{1}{3} + 2 +2 = 15 \frac{1}{3}$

Report an Error

Example Question #882 : Calculus

Find the position of an object at $t=2\pi$ if the velocity function is v(t)= cos(t) .

Possible Answers:

$\frac{\sqrt2}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

To determine the position of an object given the velocity function, integrate once to obtain the position function.

$x(t)=\int v(t)\: dt=\int cos(t)\:dt= sin(t)$

Substitute the value $t=2\pi$ into the position function.

$sin(2\pi)=0$

Report an Error

Example Question #35 : How To Find Position

Suppose the acceleration function is described by a(t)=sin(2t)+cos(t) . What is the position when $t=\frac{\pi}{2}$ ?

Possible Answers:

$\frac{\sqrt2}{2}$

$-\frac{\sqrt2}{2}$

Correct answer:

Explanation:

Obtain the position function by integrating the acceleration twice.

a(t)=sin(2t)+cos(t)

$v(t)= \int a(t)\:dt = -\frac{1}{2}cos(2t)+sin(t)$

Integrate again to obtain the position function.

$x(t)= \int v(t)\:dt= \int -\frac{1}{2}cos(2t)+sin(t)\:dt$

$x(t)=-\frac{1}{4}sin(2t)-cos(t)$

Substitute $t=\frac{\pi}{2}$ .

$x(t=\frac{\pi}{2})=-\frac{1}{4}sin\left(2\left(\frac{\pi}{2}\right)\right)-cos\left(\frac{\pi}{2}\right)=0-0=0$

Report an Error

Example Question #36 : How To Find Position

Find a vector perpendicular to (6,5) .

Possible Answers:

(-5,6)

(6,-5)

(-6,5)

(5,-6)

(-6,-5)

Correct answer:

(5,-6)

Explanation:

By definition, any vector (a,b) has a perpendicular vector (b,-a) . Given a vector (6,5) , the perpendicular vector is (5,-6) .

We can verify this further by noting that the product of any vector and its perpendicular vector is equal to , or $x\times y=0$ . Taking the product of (6,5) and (5,-6) , we get:

$(6,5)\times (5,-6)=(6\times 5)+(5\times -6)=30+(-30)=0$

Report an Error

Example Question #891 : Spatial Calculus

Find a vector perpendicular to (2,4) .

Possible Answers:

(-2,4)

(4,-2)

(-2,-4)

(2,-4)

(-4,2)

Correct answer:

(4,-2)

Explanation:

By definition, any vector (a,b) has a perpendicular vector (b,-a) . Given a vector (2,4) , the perpendicular vector is (4,-2) .

We can verify this further by noting that the product of any vector and its perpendicular vector is equal to , or $x\times y=0$ . Taking the product of (2,4) and (4,-2) , we get:

$(2,4)\times (4,-2)=(2\times 4)+(4\times -2)=8+(-8)=0$

Report an Error

Example Question #892 : Spatial Calculus

Find a vector perpendicular to (7,-12) .

Possible Answers:

(-12,-7)

(-7,12)

(-12,7)

(7,12)

(-7,-12)

Correct answer:

(-12,-7)

Explanation:

By definition, any vector (a,b) has a perpendicular vector (b,-a) . Given a vector (7,-12) , the perpendicular vector is (-12,-7) .

We can verify this further by noting that the product of any vector and its perpendicular vector is equal to , or $x\times y=0$ . Taking the product of (7,-12) and (-12,-7) , we get:

$(7,-12)\times (-12,-7)=(7\times -12)+(-12\times -7)=-84+84=0$

Report an Error

Example Question #7 : Integration

If the velocity function of a car is v(t)= 3cos(t) , what is the position when t=1 ?

Possible Answers:

3sin(1)

3cos(1)

$-\frac{9\pi}{2}$

$\frac{3\pi}{2}$

Correct answer:

3sin(1)

Explanation:

To find the position from the velocity function, take the integral of the velocity function.

$\int v(t)\:dt=\int 3cos(t)\:dt$

s(t)=3sin(t)

Substitute t=1 .

s(t=1)=3sin(1)

Report an Error

Example Question #893 : Spatial Calculus

For this question, remember that velocity is $\frac{position}{time}$ .

A particle's velocity is given by the function y=x . What is the particle's position at x = 4 ?

Possible Answers:

$\frac{x^2}{2}$

Correct answer:

Explanation:

Position is the anti-derivative of velocity, so we find the anti-derivative of the given velocity function to find the position function.

The velocity function is given as y =x , and the anti-derivative of this using the power rule is

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

$v(t)=x \rightarrow f(x)=\frac{x^{1+1}}{2}=\frac{x^2}{2}$ .

We then evaluate that function at the given point x = 4 to get,

$\frac{4^2}{2}=\frac{16}{2}=8$ .

Report an Error

View Calculus Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Calculus Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Calculus Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

All Calculus 1 Resources

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

Popular Subjects

Reading Tutors in Houston, French Tutors in Seattle, ACT Tutors in Seattle, GRE Tutors in Los Angeles, ISEE Tutors in New York City, ISEE Tutors in Los Angeles, Reading Tutors in San Diego, MCAT Tutors in San Diego, ACT Tutors in Miami, Physics Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Boston, GMAT Courses & Classes in Chicago, GMAT Courses & Classes in Seattle, GRE Courses & Classes in San Diego, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Seattle, GRE Courses & Classes in Miami, ISEE Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Chicago, ISEE Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, ISEE Test Prep in San Diego, SSAT Test Prep in Philadelphia, LSAT Test Prep in Denver, GRE Test Prep in Chicago, SSAT Test Prep in San Diego, GRE Test Prep in Denver, LSAT Test Prep in Boston

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 position

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #6 : Integration

Example Question #32 : How To Find Position

Example Question #33 : How To Find Position

Example Question #882 : Calculus

Example Question #35 : How To Find Position

Example Question #36 : How To Find Position

Example Question #891 : Spatial Calculus

Example Question #892 : Spatial Calculus

Example Question #7 : Integration

Example Question #893 : Spatial Calculus

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: