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JEE Main 2025 (29 Jan, Shift 2) · Velocity, Acceleration & Variable Motion

Velocity, Acceleration & Variable Motion question from JEE Main 2025 (29 Jan, Shift 2)

Q5JEE Main 2025 · 29 JAN · SHIFT 2Difficult

Velocity, Acceleration & Variable Motion

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 ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

  1. Relative acceleration of P w.r.t. Q is linear in tt: arel=kt+ca_{rel} = k t + c
  2. Relative displacement from the crossing at t=0t = 0: srel=ut+ct22+kt36s_{rel} = ut + \dfrac{ct^2}{2} + \dfrac{kt^3}{6}, a cubic in tt
  3. A cubic has at most 3 roots, one of which is t=0t = 0
  4. So the maximum number of crossings is 3.
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