Equations of motion are:

s = u t + 1/2 a t² ,

u = 0 and* at time t1, when the acceleration changes*, distance travelled:

s = 1/2 a t1²

v at t = t1 = u + a t = a t1

Now the acceleration is changed to -a. Then the particle continues in the same direction until the velocity becomes zero. Then the particle changes the direction and starts accelerating and passes over the point of start.

u = a t1 v = 0 acceleration = -a

v = u + a t

=> 0 = a t1 - a t => * t = t1 it takes t1 more time to stop and reverse direction.*

The distance traveled/displacement in this time:

s = u t + 1/2 a t²

=> s = a t1 * t1 - 1/2 a t1² = 1/2 a t1²

The total displacement from the initial point : 1/2 a t1² + 1/2 a t1² = a t1²

now, acceleration = -a u = 0 s = - a t1² in the negative direction

s = u t + 1/2 a t²

=> - a t1² = 0 - 1/2 a t²

=>* t = √2 t1*

The total time T from initial point forward till back to initial point :

* T = 2 t1 + √2 t1 = (2 + √2) t1*