Physics · Class 11

Uniform vs changing motion

Cart A covers equal displacements in equal time intervals because its velocity is constant. Cart B has a changing velocity when its acceleration is nonzero. Their position graphs can cross even when their slopes differ.

Open the interactive experiment →

Equal positions do not imply equal velocities.

சீரான இயக்கத்தில் சம நேரங்களில் சம இடப்பெயர்ச்சிகள் ஏற்படும். முடுக்கம் உள்ள வண்டியின் திசைவேகம் மாறும். இரு வண்டிகளின் நிலை ஒரே நேரத்தில் சமமாக இருந்தாலும் திசைவேகங்கள் சமமாக வேண்டியதில்லை.

Key notes, relationships and model limits

Key relationship

xA = vA t; xB = uB t + ½aB t²; vB = uB + aB t

Remember

Common trap

The crossing of two position graphs means equal positions, not equal velocities.

Model limits

Both carts start at x = 0; A has constant velocity; B has constant acceleration; carts pass through each other without collision. Signed motion may reverse.

What you will learn

Identify uniform motion from a straight position graph; compare simultaneous positions and velocities.

Try the experiment

Play the catch-up preset. At the graph intersection compare A’s slope with B’s slope. Set acceleration to zero.

Think of it this way

A steady cyclist and a runner gathering speed can meet while moving at different speeds.

Worked example

A: x = 5t. B: x = t + ½t². Besides t = 0 they meet at t = 8 s and x = 40 m. A has v = 5 m/s; B has v = 9 m/s.

Why this matters

Separating position from rate of change helps interpret traffic and race graphs.

Before you start

Signed numbers · coordinates · gradients · area under a graph

Check your understanding

A cart has x = 5t m. What does its position graph show?

Increasing acceleration
Constant velocity +5 m/s
A stationary cart

Read the explanation

The gradient dx/dt is +5 m/s at every time; acceleration is zero.

Course connection: CBSE XI Chapter 2; NEET and JEE Main Unit 2; JEE Advanced Mechanics. Check the selected syllabus for relative-velocity scope.