Question

Two objects moving along the same straight line are leaving point a with an acceleration a, 2a and velocity 2u, u respectively at time t = 0. The distance moved by the objects with respect to point a when one object overtakes the other is ku2aku2a where k is

Answer 1

Explanation:

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 2nd

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