Abody moves along a straight line, its distance from the origin at any instant being given by the equation x = 8t − 3t2, where x is in centimeters and t is in seconds.

(a) find the average velocity of the body in the interval from t = 0 to t = 1 sec, and in the interval from t = 0 to t = 4 sec.
(b) find the expression for the average velocity in the interval from t to t + δt.
(c) what is the limiting value of this expression as δt approaches zero?
(d) find the time or times at which the body is at rest.
(e) find the expression for the acceleration at any time.