Acceleration: the rate of change of velocity

5 minAS Level2.1.1

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

By the end of this lesson

By the end you can define acceleration, calculate it from a change in velocity, and use a sign convention to tell speeding up from slowing down.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$\Delta$	a change in, so $\Delta v$ means "the change in $v$ "

Fast is not the same as accelerating

An airliner cruising at a steady $250\ \text{m s}^{-1}$ in a straight line has zero acceleration. A sprinter exploding out of the blocks at a measly $2\ \text{m s}^{-1}$ has a large one.

Acceleration doesn't care how fast you are going. It cares how fast your velocity is changing.

Definition

Acceleration

The rate of change of velocity (the change in velocity per unit time):

$a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$

where $u$ is the initial velocity and $v$ the final velocity after time $t$ . It is a vector, measured in $\text{m s}^{-2}$ .

What "m s⁻²" actually means

Read $\text{m s}^{-2}$ as "metres per second, every second". An acceleration of $3\ \text{m s}^{-2}$ adds $3\ \text{m s}^{-1}$ to the velocity each second:

time / s	0	1	2	3
velocity / $\text{m s}^{-1}$	0	3	6	9

Worked example: A car pulls away

A car accelerates uniformly from rest to $27\ \text{m s}^{-1}$ in $9.0\ \text{s}$ . Find its acceleration.

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Quick check

DefinitionQuestion 1 · Recall

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