For a particle moving in a straight line, the velocity varies with time according to v(t)=3t2−12t+5 (SI units) for 0≤t≤5s.
(i) Sketch the v–t curve for the given time interval, clearly indicating the intercepts on the axes and the turning point.
(ii) Calculate the instantaneous acceleration at t=1s and at t=4s.
(iii) At each of the two instants above, state whether the particle is speeding up or slowing down and give a reason based on your results.