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here the acceleration and the time interval in all three parts is the same
part 1
the body starts from rest with acceleration 'a' and attains a velocity 'v1' after t = 5 seconds
so,
s1 = 0 + (1/2)at2 (1)
and
v1 = 0 + at
or
v1 = at (2)
part 2
the body has an initial velocity v1 and accelerates to v2 after t = 5seconds
s2 = v1t + (1/2)at2
or from eq (2)
s2 = at.t + (1/2)at2
thus,
s2 = (3/2)at2 (3)
v2 = v1 + at
v2 = at + at = 2at (4)
part 3
the body has an initial velocity 'v2' and accelerates to 'v3' after t = 5 seconds
s3 = v2t + (1/2)at2
or from equation (4)
s3 = 2at.t + (1/2)at2
so
s3 = (5/2)at2 (5)
now from equations (1), (3) and (5) we confirm that
s1 = s2/3
s1 = s3/5
s2/s3 = 3/5
5s2 = 3s3
s2/3= s3/5
thus, finally we get
s1 = s2/3 = s3/5
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