A lorry and a car moving with the same momentum are brought to rest by the application of brakes , which provide equal retarding force . Which of them will come to rest in shorter time ? Which will come to rest in less distance ?

Explanation

Momentum `(bar(P)=mv)` is same for both lorry and car .
Work done to stop a body = Kinetic energy stored
`thereforeW=F.S=(1)/(2)mv^(2)` = K.E . But force applied
by brakes is same for lorry and car .
Relation between `bar(P)` on K.E. is
`K.E=(P^(2))/(2m)=F.S`
or stopping distance `S=vec(P^(2))/(2mF)`
`becausebar(P)andbar(F)` are same `Sprop(1)/(m)`
So lighter body (car ) will travel longer distance when P , F are same
Then mS = constant .
`therefore` So car travels longer distance than lorry before it is stopped .