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

Question

Two cars $P$ and $Q$ are moving on a road in the same direction. Accleration of car $P$ increases linearly with time whereas car $Q$ moves with a constant accleration. 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 ________.

Aicharya · Accepted Answer

$\mathrm{a}_{\mathrm{p}}=\mathrm{kt}, \mathrm{k}$ is constant
$\mathrm{a}_{\mathrm{Q}}=\mathrm{a}, \mathrm{a}$ is constant
$\mathrm{a}_{\mathrm{QP}}=\mathrm{a}_{\mathrm{Q}}-\mathrm{a}_{\mathrm{p}}=\mathrm{a}-\mathrm{kt}$
as initial velocities are not mentioned in question, so will have to assume two cases.
Case-I
$\mathrm{u}_{\mathrm{OP}}$ and $\mathrm{a}_{\mathrm{QP}}$ in same direction

Total number of crossing $=2$ Case-II
$\mathrm{u}_{\mathrm{QP}}$ and $\mathrm{a}_{\mathrm{QP}}$ in opposite direction

Total number of crossing $=3$

Two cars $P$ and $Q$ are moving on a road in the same direction. Accleration of car $P$ increases linearly…

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