Question

A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.27t^2...

A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.27t^2 + 16t feet per second after t seconds (for 0 ≤ t < 30).

(a) Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time t = 0.]

D(t) =

(b) Use the formula that you found in part (a) to find the distance that the car will travel in the first 10 seconds.

ft.

Homework Answers

Answer #1

we are given

(a)

we can find antiderivative for finding distance

we can use power rule

we are given

D(0)=0

now, we can plug it back

and we get

.........Answer

(B)

we can plug t=10

..........Answer

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