An object moves along a straight line. Its displacement s (in metres) from a reference point at time t (in seconds) is given by s=4 t^{3}-21 t^{2}+18 t \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) Find any times at which the velocity of the object is zero. (c) The minimum velocity occurs when the acceleration is zero. Show thatthis happens at time t = 7 seconds, and find the value of this minimumvelocity.