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?

Explanation

Let the car and bike will meet after covering a distance S in a time .t. sec.
For car `S=1/2 at^(2) ……(1)`
for bike S=ut ……..(2)
Since they cover same distance
`ut=1/2 at^(2) rArr t=(2u)/a`
The car and bike will meet after a time of `(2u)/a` sec
The velocity of car after .t. sec is
`V_("car")=at=a((2u)/a)=2u`
The velocity of car w.r.t. bike is `V_("rel")=2u-u=u`