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  4. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x P ( t )= at + bt 2 and x Q ( t )=f t - t 2. At what time do the cars have the same velocity ?

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Q. Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x _{ P }( t )= at + bt ^{2}$ and $x _{ Q }( t )=f t - t ^{2}$. At what time do the cars have the same velocity ?

NEETNEET 2016Motion in a Straight Line

Solution:

$v_{p} = \frac{dx_{p}}{dt} = a +2bt $
$ v_{Q} = \frac{dx_{Q}}{dt} = f - 2t $
$ v_{P} = v_{Q} \Rightarrow a +2bt =f-2t$
$ t =\frac{ f-a}{2\left(b+1\right)} $