For 0≤t≤8 seconds, the acceleration (in meters per second squared) of a toy car moving along a straight path is modeled by a(t)=4sin(8πt). At time t=0, the velocity of the car is −3 m/s.
(a) Determine an expression for the velocity v(t) of the car for 0≤t≤8.
(b) Compute the car’s average velocity, in meters per second, over the interval 0≤t≤8. Show all steps leading to your answer.
(c) Interpret the sign of the average velocity found in part (b) within the context of the car’s motion, and state whether the car is, on average, moving forward or backward during the interval.