Verified Solution • 2025–26 Session moderate

QNEET-2016-Ph-1143: NEET 2016 Physics - Class 11 NEET-2016-Ph-1143 Solution: Two cars P and Q start from a point at the same time in a…

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) = (ft - t^2)

. At what time do the cars have the same velocity?

\frac{a-f}{1+b}

\frac{a+f}{2(b-1)}

\frac{a+f}{2(1+b)}

\frac{f-a}{2(1+b)}

Multiple Choice Options

A ${{a - f} \over {1 + b}}$ 1 + b a _ f _
B ${{a + f} \over {2\left( {b - 1} \right)}}$ 2 ( b _ 1 ) a + f _
C ${{a + f} \over {2\left( {1 + b} \right)}}$ 2 ( 1 + b ) a + f _
D ${{f - a} \over {2\left( {1 + b} \right)}}$ 2 ( 1 + b ) f _ a _

Step-by-Step Verified Solution

For car P, x P (t) = (at + bt 2 ) v P (t) = d x p ( t ) d t = a + 2bt Similarly for car Q, x Q (t) = (ft - t 2 ) v Q (t) = d x Q ( t ) d t = f - 2t When they have same velocity then, v P (t) = v Q (t) _ a + 2bt = f - 2t _ 2t(b + 1) = f - a _ t = f _ a 2 ( 1 + b )

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