An object travels along a straight line. The function s(t) = -32t^2 - 6t + 45 gives the object's position, in feet, at time t seconds. Write a function that gives the object's velocity v(t) in feet per second. v(t) = ______

Differentiate s(t) for v(t): To find the velocity function v(t), we need to differentiate the position function s(t) with respect to time t.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An object travels along a straight line. The function $s(t) = -32t^2 - 6t + 45$ gives the object's position, in feet, at time $t$ seconds. $\newline$ Write a function that gives the object's velocity $v(t)$ in feet per second. $\newline$ v(t) = ______

View step-by-step help

Home

Math Problems

Calculus

Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. An object travels along a straight line. The function

s(t) = -32t^2 - 6t + 45

gives the object's position, in feet, at time

t

seconds.

\newline

Write a function that gives the object's velocity

v(t)

in feet per second.

\newline

v(t) = ______

Differentiate $s(t)$ for $v(t)$ : To find the velocity function $v(t)$ , we need to differentiate the position function $s(t)$ with respect to time $t$ .

More problems from Relate position, velocity, speed, and acceleration using derivatives

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{0.7} \sin (2 t+3)

. What is the acceleration of the particle at time

t=4

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{1.1} \cos \left(t^{2}-5\right)

. If the position of the particle is

x=-2

when

t=2.5

, what is the position of the particle when

t=1

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{0.9} \sin (t-1)

. If the position of the particle is

x=-3

when

t=3

, what is the position of the particle when

t=5

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{2.1} \sin (2 t)

. Find all times when the speed of the particle is equal to

2

on the interval

0 \leq t \leq 4

. You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

t=

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=\left(t^{2.3}+5\right) \sin (2 t)

. What is the distance traveled by the particle over the interval

0 \leq t \leq 5

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{1.9} \cos (3 t-1)

. What is the distance traveled by the particle over the interval

0 \leq t \leq 3

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=\left(t^{1.6}+3\right) \cos (3 t)

. What is the average velocity of the particle on the interval

0 \leq t \leq 6

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its acceleration is given by

a(t)=\left(t^{0.5}+3\right) \cos (3 t)

. If the velocity of the particle is

v=-2

when

t=1

, what is the velocity of the particle when

t=1

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=t^{2.1} \sin (2 t+5)

. Find all times when the speed of the particle is equal to

1

on the interval

0 \leq t \leq 3

. You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

t=

Get tutor help

Posted 9 months ago

Question

A particle travels along the

x

-axis such that its velocity is given by

v(t)=\left(t^{2.1}+5\right) \cos (2 t)

. What is the distance traveled by the particle over the interval

0 \leq t \leq 5

? You may use a calculator and round your answer to the nearest thousandth.

\newline

Answer:

Get tutor help

Posted 9 months ago

View all (107)

An object travels along a straight line. The function s(t)=−32t2−6t+45s(t) = -32t^2 - 6t + 45s(t)=−32t2−6t+45 gives the object's position, in feet, at time ttt seconds.\newlineWrite a function that gives the object's velocity v(t)v(t)v(t) in feet per second.\newlinev(t) = ______

An object travels along a straight line. The function $s(t) = -32t^2 - 6t + 45$ gives the object's position, in feet, at time $t$ seconds. $\newline$ Write a function that gives the object's velocity $v(t)$ in feet per second. $\newline$ v(t) = ______