Physics · Motion in one Dimension

JEE Main 2025 — 29 January, Evening Shift — Question 41

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 $\mathrm{t}=0$ ) is $\_\_\_\_\_$ .

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{a}_{\mathrm{p}}=\mathrm{kt}, \mathrm{k}$ is constant $a_{Q}=a, a$ 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 $\mathrm{u}_{\mathrm{or}}$ 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 $=3$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Evening Shift
Subject: Physics
Chapter: Motion in one Dimension
Topic: Non-Uniformly Accelerated Motion