In this problem point starts moving with uniform acceleration a and after time t (Position B ) the direction of acceleration get reversed i.e. the retardation of same value works on the point. Due to this velocity of points goes on decreasing and at position C its velocity becomes zero. Now the direction of motion of point reversed and it moves from C to A under the effect of acceleration a .

We have to calculate the total time in this motion. Starting velocity at position A is equal to zero.

Velocity at position B ⇒ ⇒ at [As u = 0]

Distance between A and B,

As same amount of retardation works on a point and it comes to rest therefore

and time required to cover this distance is also equal to t .

Total time taken for motion between A and C = 2 t

Now for the return journey from C to A

⇒ ⇒ ⇒ ⇒

Hence total time in which point returns to initial point