Velocity–time graphs and acceleration

5 minAS Level2.1.22.1.5

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

By the end of this lesson

By the end you can read a velocity–time graph, find the acceleration from its gradient (using a tangent on a curve), and interpret a line that dips below the time axis.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$\Delta$	a change in, so $\Delta v$ means "the change in $v$ "
$v$	final velocity
$t$	time
$a$	acceleration

Same axes, different story

A velocity–time graph looks like a displacement–time graph's twin, but it tells a different story. Mixing them up is the number one graph crime in AS Physics.

Here the gradient is

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

which is the definition of acceleration. So the gradient of a velocity–time graph is the acceleration.

Worked example: Reading the car's graph

Find the car's acceleration in each section of the graph.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Recall

Answer the 2 questions above to continue.