The velocity. v ms". of a particle. travelling in a straight line. at time t s after leaving a fixed point 0. is given by r = 31'2 l8: 4- 32. when: l a: 0. Find (i) the value of t for which the acceleration is zero. (ii) the distance of the particle from 0 when its velocity is a minimum. [5] A car moves on a straight road. As the driver passes a point A on the road with a speed of 20 ms '. he notices an accident ahead at a point 3. He immediately applies the brakes and the car moves with an acceleration of a ms'i where a = - 6 and t is the time after passing A. 2 When i = 4. the car passes the accident at B. The car then moves with a constant acceleration of 2 ms" until the_ original speed of 20 ms" is regained at a point C. Find (i) the speed of the car at 3. I4] { ii) the distance AB. [3] (iii) the time taken for the car to travel from B to C. [2] Sketch the velocity-time graph for thejoumey from A to C. ' l2] A cyclist starts from rest from a point A and travels in a straight line until he comes to rest at a point B. During the motion, his velocity, v ms", is given by v = 61 - r, where ? is the time in seconds after leaving A. Find i) the time taken for the cyclist to travel from A to B. (ii) the distance AB, [3] (iii) the acceleration of the cyclist when / = 8. [2]