The velocity of a particle moving along a straight path is described by
v(t)=3t2−12t+9(t in seconds,v in m s−1).
Based on this information, answer the following:
(i) Obtain the acceleration a(t) of the particle.
(ii) Find the value(s) of t for which the particle is at rest.
(iii) Determine the acceleration of the particle at each instant found in part (ii) and comment on the nature of motion near those instants.