a particle starts from rest ad moves a distance S1 with a constant acceleration in time T if this particle - Science - Motion

Question

a particle starts from rest ad moves a distance S1 with a
constant acceleration in time T if this particle travel distance S2
in the next time t then show that s2=3s1

Vineet Kumar · Answer

S
1 = ut + ½
at 2
u= 0
t= T
S
1 = ½
aT 2
…(1)
now
2aS
1 =
v 2
–u
2
i e 2 x a x ½ at
2 =
v 2
or v= at … (2)
now when the particle travels the distance S2 again using
equations of motion
S
2 = ut + ½
at 2
where now u= at {from euation (1)}
so S
2 = at +
1/at 2
or S
2 = 3/2
at 2
… (3)
comparing equation (1) and (3)
S
2 =
3S 1

a particle starts from rest ad moves a distance S1 with a constant acceleration in time T if this particle travel distance S2 in the next time t then show that s2=3s1