Question

A body travels for 15s starting from rest with constant acceleration. If it travels distances S1, S2 and S3 in the first five seconds, second five seconds and next five seconds respectively, the relation between S1, S2 and S3 is - (a) S1=S2=S3 (b) 5S1=3S2=S3 (c) S1=S2/3= S3/5 (d) S1=S2/5=S3/3

Answer 1

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

which is option (c)