Problem

A particle moves in a straight line with constant acceleration

a

. The displacements of particle from origin in times

t_1

t_2

and

t_3

are

s_1

s_2

and

s_3

respectively. If times are in AP with common difference

d

and displacements are in GP, then prove that

a = \frac{(\sqrt{s_1} - \sqrt{s_3})^2}{d^2}