(a) A particle has an initial velocity of u ms. It moves in a straight line with...

(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.