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 there will they meet ? What is the velocity of car with respect to the bike at the time of meeting?

Explanation

`underset("car")(s)=(1)/(2)at^(2)to(1),underset("bike")(s)=ut to(2)`
if they meet at the same point
`underset("car")(s)=underset("bike")(s)`
`(1)/(2)at^(2)=ut impliest=(2u)/(3)` ltbr `S_("bike")=ut=u(2u)/(a)=(2u^(2))/(a)`
`V_("car")=at=2u`
`V_("car")` w.r.t. bike at the time of meeting,
`|vec V_(cb)|=|vec(V)_("car")-vec(V)_("bike")|=2u-u=u`