Mechanics · Kinematics
Chapter 1 · 4
The idea
Motion graphs (displacement–time & velocity–time)
What the gradient and the area mean on each kind of motion graph — gradient of displacement–time is velocity, gradient of velocity–time is acceleration, area under velocity–time is displacement — and how to model a journey as a graph and read unknowns off its area.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Mechanics · Kinematics
Motion graphs (displacement–time & velocity–time)
What the gradient and the area mean on each kind of motion graph — gradient of displacement–time is velocity, gradient of velocity–time is acceleration, area under velocity–time is displacement — and how to model a journey as a graph and read unknowns off its area.
Why it works
Two graphs, two meanings
A motion graph turns a whole journey into one picture. There are two kinds, and the single most important skill in this topic is keeping straight what the gradient and the area mean on each — because they mean different things.Displacement–time: gradient is velocity
The graph ( up the side, along the bottom) tells you where the particle is at each instant. Its gradient is the velocity — because velocity is exactly the rate at which displacement changes, . So:- a straight line = constant velocity (steeper = faster);
- a horizontal line = gradient = the particle is at rest (still moving through time, but not through space);
- a negative gradient = moving back towards the start;
- a curve = changing velocity, i.e. acceleration.
Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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