A body starts from rest and moves with uniform acceleration. If the distance travelled by it in the first 2 ~s is x₁ and in the next 2 ~s is x₂ , then x₁ and x₂ are related as

Step-by-step solution

If a be the acceleration of the body, then distance travelled by the body in 2 ~s is given as, gathered x₁=u t+ 1 2 a t^2=0 2+ 1 2 a (2)^2 x₁=2 a gathered Velocity of body at the end of 2 ~s is given as, aligned & v=u+a t=0+a 2 & v=2 a aligned Distance travelled by the body in next 2 ~s is given as, aligned & x₂=v t+ 1 2 a t^2 & =2 a 2+ 1 2 a (2)^2 [from Eq. (ii)] & =4 a+2 a & x₂=6 a=3 2 a & x₂=3 x₁ [from Eq. (i)] & x₂=3 x₁ & aligned