IXL - Relate position, velocity, speed, and acceleration using integrals (Calculus practice)

An object is moving in a straight line with acceleration

(

)

yards per second squared at time

seconds.

Which expression represents the change in the object's velocity from

second to

seconds?

∫

–

∫

–

(

)

∫

(

)

What is the change in the object's velocity from

second to

seconds?

Round your answer to the nearest tenth.

yards per second

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Learn with an example

question

An object is moving in a straight line with acceleration

(

)

–

meters per minute squared at time

minutes.

Which expression represents the change in the object's velocity from

minute to

minutes?

∫

–

∫

–

∫

–

(

–

)

∫

(

–

)

What is the change in the object's velocity from

minute to

minutes?

Round your answer to the nearest tenth.

meters per minute

key idea

At time

an object's

acceleration,

(

)

is equal to the instantaneous rate of change of its velocity,

(

)

(

)

′

(

)

To find the object's change in velocity from time

to time

you can integrate its acceleration.

∫

(

)

By the Fundamental Theorem of Calculus, Part 2

(

)

–

(

)

By the Fundamental Theorem of Calculus, Part 2

solution

Find the change in the object's velocity from

minute to

minutes. Substitute

and

(

)

–

into the formula for change in velocity.

change in velocity

∫

(

)

∫

(

–

)

Evaluate the integral.

∫

(

–

)

–

(

)

–

(

)

–

(

)

–

(

)

–

100

33.3333…

Rounded to the nearest tenth, the change in the object's velocity from

minute to

minutes is 33.3 meters per

minute.

$Confetti$

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Not feeling ready yet? These can help:

K.1Relate position, velocity, speed, and acceleration using derivatives

T.4Evaluate definite integrals: mixed review

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