Question

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.

Answer 1

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.