A body starts moving from rest with constant acceleration covers displacement S 1 in first ( p - 1 ) seconds and S 2 in first p seconds. The displacement S 1 + S 2 will be made in time :

Step-by-step solution

For the displacement S 1 of the body, it can be written that S 1 = 1 2 a ( p - 1 ) 2 . . . 1 And, for the displacement S 2 of the body, it follows that S 2 = 1 2 a ( p ) 2 . . . 2 If t be the required time, it follows that S 1 + S 2 = 1 2 a t 2 . . . 3 Equations (1), (2) and (3) imply that ( p - 1 ) 2 + p 2 = t 2 ⇒ t = 2 p 2 - 2 p + 1 s