Two cars P and Q are moving on a road in the same diretion. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of c

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Solution

Q.
Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is __________. [2025]

Ans.
(3)

For first car P $\to$ acceleration ( $a_{P}$ ) = ct, c is constant

For second car Q $\to$ acceleration ( $a_{Q}$ ) = a, a is constant

Let us analyse the problem in two cases

Case I:

$\Rightarrow$ $u_{Q P}$ and $a_{Q P}$ in same direction

They cross 2 times in this case

Case-II:

$a_{Q P}$ and $u_{Q P}$ in opposite direction

They cross 3 times in this case.

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