(a) A particle has an initial velocity of u ms?¹. It moves in a straight line with constant acceleration f for 4 seconds. It travels 52 m while accelerating. The particle then moves with uniform velocity and travels 48 m in 3 seconds. It is then brought to rest by a constant deceleration of 2f.

Find

(i) the value of u

(ii) the deceleration of the particle

(iii) the total distance travelled by the particle.

(b) Car A and car B travel in the same direction along a straight horizontal road. Car A starts from rest at a point P and moves with constant acceleration a ms?². Five seconds later, car B passes point P with constant speed u ms?¹.

(i) Find the value of u, in terms of a, if car B just catches up with car A.

(ii) Find, in terms of u and a, the greatest distance that car B is ahead of car A when u > 10a.

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