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A car starts from rest and moves with un...

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?

Text Solution

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`underset("car")s = (1)/(2)at^(2) to (1), underset("bike") = ut to (2)`
if they meet at the same point
`underset("car")s = underset("bike")`
`(1)/(2)at^(2) = ut rArr t = (2u)/(a)`
`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)| = |vecv_("car") - vecv_("bike")| = 2u - u = u`
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