Question

Two objects moving alone the same straight line are leaving point A with an acceleration a, 2a & velocity 2u, u at time t = 0 sec. The distance moved by thr object with respect to point A when one object overtakes the other is :-

(A) 6u²/ a

(B) 2u²/ a

(C) 4u²/ a

(D) None of these

Answer 1

Let t be the time when the 2nd object overtake the 1st

For the first object distance travelled will be

S₁ = ut + ½ at² ---1.

For the 2nd object distance travelled will be

S₂ = 2ut + ½ (2a)t²

=> S₂ = 2ut + at² ---2.

So at time t distance travelled by the first object must be equal to that travelled by the 2^nd

S₁ = S₂

ut + ½ at² = 2ut + at²

=> ut- ½ at² = 0

=> t(u- ½ at) = 0

=> t = 2u/a

Now distance travelled when the bodies overtake will be

d = u× t = u×2u/a = 2u²/a