An object starting from rest accelerates uniformly to cover s1 distance in 2 seconds and s2 distance in next 2 seconds.
Show that 3s1=s2.
we know that
s = ut + (1/2)at2
In the first case
u1 = 0 m/s
t1 = 2s
so, distance travelled in first 2s
s1 = 0 + (1/2).a.22
or
s1 = 2a ..............................(1)
and
the velocity after 2s will be
v1 = u + at1 = 0 + a.2
or
v1 = 2a
now,
in the second case
u2 = v1 = 2a
t2 = 2s
so,
s2 = 2a.2 + (1/2).a.22
= 4a + 2a
so,
s2 = 6a ..............................(2)
now,
from (1) and (2), we get
s1 / s2 = 2a / 6a
or
3s1 = s2
which is the required answer.