Q. A body starts with an initial vel. of 10 m/s and moves along a st. line with a constant acceleration. When the vel. of the particle is 50 m/s, acc. is reversed in direction. Find vel. of particle when it reaches the starting point.

from SYMMETRY it is clear that the velocity at the starting point is 10 m/s in the opposite direction.

let its accln = a & after time t its velocity is 50 and accln is reversed

Ui = 10m/s, Uf  = 50m/s

  50 = 10 + at

or at=40 ........................(i)

now its velocity reduces to 0

0=50 - aT             ( accln is reversed)

or aT=50 .........................(ii)

when it reaches to initial point

then for reverse motion 

v` = 0+ a(t+T)

    = 90m/s