If the velocity v of a particle moving along a straight line

If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 47 m/s to a value approaching zero at s = 32 m, determine the acceleration a of the particle when s= 15 m and show that the particle never reaches the 32-m displacement.

Solution

Given : Decreasing velocity is = -47 m/s

Its value approaches to zero i.e. final velocity = 0 m/s

Distance travelled = 32 m

Acceleration a = v² - u² / 2s

= 0-2209 / (2*32)

= -34.51 m/s2

At s=15m a = 34.51m/s2 only as velocity while decelerating changes with constant rate by which velocity remains constant.