a body travels for 15 sec starting from rest with constant acclerations if it travels distance s1 s2 s3 in the first five second second five seconds and next five seconds respectively the relation between s1,s2 and s3 is

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

so,

s2 = v1t + (1/2)at2

or from eq (2)

s2 = at.t + (1/2)at2

thus,

s2 = (3/2)at2    (3)

and

v2 = v1 + at

or

v2 = at + at = 2at  (4)

part 3

the body has an initial velocity 'v2' and accelerates to 'v3' after t = 5 seconds

so,

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

and

s1 = s3/5

and

s2/s3 = 3/5

5s2 = 3s3

or

s2/3= s3/5

thus, finally we get

s1 = s2/3 = s3/5