Mathematics

Problem

An automobile traveling on a straight test track has acceleration

a(t)=4\sin\!\bigl(\tfrac{\pi t}{5}\bigr)-2

(in m/s

^{2}

) for

0\le t\le 10

seconds. The initial velocity is

v(0)=3

m/s, and the initial position is

s(0)=0

. (a) Determine expressions for the velocity

v(t)

and for the displacement

s(10)-s(0)

. (b) Compute the automobile’s average acceleration on

0\le t\le 10

seconds and state the units. (c) Find the automobile’s average velocity on the same interval. (d) Find all times

c

(0,10)

at which the instantaneous acceleration equals the average acceleration found in part (b). Justify your answer.