MHT-CET Physics · Motion in a Plane

Relative Motion and Meeting Problems

Two moving bodies are handled by watching one from the other — their relative velocity is the difference of their velocities — or by writing each position as a function of time and asking when the positions, or the velocities, are equal.

All Motion in a Plane notes MHT-CET Physics strategy

Why this matters

7 PYQs, none HARD: two trains crossing, two cars whose velocities become equal, a uniformly accelerating body catching a steady one, and a runner who must cut across to meet another running at right angles. One card.

Concept 1 of 1: Relative Velocity and Meeting

Two trains passing each other must together cover the sum of their lengths at their relative speed: the sum of speeds if opposite, the difference if the same way. Two bodies starting together meet when their displacements are equal: a steady V and an accelerating a meet at t = 2V/a. Their velocities are equal when the derivatives of the positions match. A runner at A meeting one who starts at B and runs perpendicular to AB covers the hypotenuse: (v t)² = b² + (v₁t)², so t = b/√(v² − v₁²).

Definition

Crossing: $t = \dfrac{L_1 + L_2}{v_{\text{rel}}}$ , $v_{\text{rel}} = v_1 + v_2$ (opposite) or $|v_1 - v_2|$ (same way).
Meeting from the same start: equal displacements ( $\tfrac{1}{2}at^2 = Vt$ ⇒ $t = \dfrac{2V}{a}$ ).
Equal velocities: equal derivatives ( $a + 2bt = F - 2t$ ⇒ $t = \dfrac{F - a}{2(1 + b)}$ ).
Gap when velocities match (u steady, a from rest): $\dfrac{u^2}{2a}$ .
Perpendicular chase: $t = \dfrac{b}{\sqrt{v_2^2 - v_1^2}}$ .

Relative velocity

\vec{v}_{AB} = \vec{v}_A - \vec{v}_B

Worked example

A car at a steady 20 m/s passes a scooter at rest, which then accelerates at 2 m/s². When and where does the scooter catch up?

Practice this conceptself-check · 1 quick reps

The same idea in a real exam question:

MHT-CET · 2025 · 25 April Shift II · Q19Moderate

Example 1 · Motion in a Plane · Relative Motion and Meeting Problems

Two girls are standing at the ends '

A

' and '

B

' of a ground where

AB = b

. The girl at ' B ' starts running in a direction perpendicular to ' AB ' with velocity '

V_{1}

'. The girl at ' A ' starts running simultaneously with velocity '

V_{2}

' and in shortest distance meets the other girl in time '

t

'. The value of '

t

' is

Using the sum of speeds for trains going the same way

Same direction: the faster gains only by the DIFFERENCE of speeds. Opposite directions: the sum.

Forgetting both train lengths

Crossing is complete when the rear of one passes the rear of the other: the distance is the sum of the two lengths.

Drill 6 more on relative velocity and meeting

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Relative Velocity and Meeting
Relative velocity
$\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$

Watch out for (2)

Using the sum of speeds for trains going the same way
→ Relative Velocity and Meeting
Forgetting both train lengths
→ Relative Velocity and Meeting

Test yourself on Motion in a Plane

15 past MHT-CET questions from this chapter, timed at 14 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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