A body moves along a straight line so that its displacement from the origin at time t is
x(t)=t4−4t2+3 metres,
where t is in seconds. Consider the interval 0≤t≤3 s.
(a) Derive expressions for the instantaneous velocity and instantaneous acceleration of the body.
(b) Find the instant(s) within the given interval when the acceleration becomes zero. For each such instant, state whether the body is speeding up or slowing down immediately after that instant.
(c) Determine the exact instant(s) in the interval when the body reverses its direction of motion.
(d) Calculate the total distance travelled by the body during the interval 0 s to 3 s.