Definition

Acceleration

a = \frac{d v}{d t}

Statement

The instantaneous rate of change of velocity with time.

Symbols and units

$a$	instantaneous acceleration	m/s²
$v$	velocity	m/s

When it applies

Any motion; a is the derivative of velocity with respect to time.

Derivation

The same limiting process applied to velocity instead of position:

a = Δ t \to 0 lim \frac{Δ v}{Δ t} = \frac{d v}{d t}

Worked examples

Acceleration from a velocity graph

v(t) = 3t² (m/s):

a (t) = \frac{d v}{d t} = 6 t

At t = 2 s:

a = 12 m/s^{2}

Watch out for

Acceleration is non-zero whenever velocity changes in direction, even at constant speed — as in uniform circular motion.

Connects to