Question

A car starts from rest and moves with uniform acceleration 'a'. At the same instant from the same point a bike crosses with a uniform velocity 'u'. When and where will they meet? What is the velocity of car with respect to the bike at the time of meeting?

Please solve with relative motion concept.

Answer 1

Let them meet after time t

We shall use the equation of motion s= u t + 0.5 a t^2,

Distance travelled by bike , B = u t , where u= uniform velocity ( a=0) of bike

Distance travelled by car, C = 0.5 a t^2 , where a= uniform acceleration of car , ( initial velocity=0)

Equating the two distances, B=C, we get t= 2 u/a

Distance travelled upto meeting point = u t = u ( 2u/a) =( 2 u^2)/a

Velocity of car in time t, v= at= a .2 .u/a= 2u

Velocity of car with respect to bike at the point of meeting = 2u-u=u