A particle starts from rest and traverses a distance 2 x with uniform acceleration, then moves uniformly over a further distance 4 x and finally comes to rest after moving a further distance 6 x under uniform retardation. Assuming entire motion to be rectilinear motion, the ratio of average speed over the journey to the maximum speed on its way is

Step-by-step solution

Let t 1 , t 2 and t 3 be the time taken by the particles to cover the distance 2 x , 4 x and 6 x respectively. Let v be the velocity of the particle at B ie , maximum velocity. The particle moves with uniform acceleration from A to B . For motion from A to B . Average velocity = 0 + v 2 = v 2 Time taken, t 1 = 2 x v 2 Particle moves with uniform retardation from C TO D , V avg = 0 + v 2 = v 2 Time taken , t 3 = 6 x ( v 2 ) Total time = t 1 + t 2 + t 3 t = 2 x v 2 + 4 x v + 6 x v 2 = 20 x v Average Velocity over = 6