Displacement–time graphs

5 minAS Level2.1.22.1.4

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can read a displacement–time graph like a story and find the velocity from its gradient, including on a curve, by drawing a tangent.

The gradient is the velocity

Plot displacement $s$ up the side and time $t$ along the bottom. The gradient of the line is

$\text{gradient} = \frac{\Delta s}{\Delta t}$

and change in displacement per unit time is exactly the definition of velocity. So the gradient of a displacement–time graph is the velocity. No extra formula needed.

Reading the shapes

What the line does	What the object does
horizontal	at rest ( $v = 0$ )
straight, sloping up	constant velocity, positive direction
steeper straight line	constant velocity, but faster
straight, sloping down	constant velocity in the negative direction (heading back)
curving, getting steeper	speeding up
curving, getting flatter	slowing down

Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Recall

Answer the 2 questions above to continue.