An object moves along a straight line. Its displacement s (in metres) from areference point at time t (in seconds) is given by s=t^{4}-3 t^{3}+3 t^{2} \quad(t \geq 0) Answer

the following questions using calculus and algebra. You may find it helpful to sketch or plot graphs, but no marks will be awarded for graphical arguments or solutions. (a) Find expressions for the velocity v and the acceleration a of the object at time t. (b) Show that the velocity of the object is zero only at time t = 0. (c) Find any time period or periods over which the velocity of the object is increasing.