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.
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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