Concept Library / Kinematics

Acceleration

Acceleration is the rate of change of velocity. Average acceleration over a time interval is

a_{avg} = \frac{Δ v}{Δ t} = \frac{v - u}{Δ t} .

Instantaneous acceleration is the acceleration at one instant; graphically it is the gradient of the tangent to a velocity-time graph.

Full explanation

Acceleration is the rate of change of velocity. Average acceleration over a time interval is

a_{avg} = \frac{Δ v}{Δ t} = \frac{v - u}{Δ t} .

Instantaneous acceleration is the acceleration at one instant; graphically it is the gradient of the tangent to a velocity-time graph.

Acceleration describes how rapidly velocity changes. Because velocity includes direction, an object can accelerate by speeding up, slowing down, or changing direction. A negative acceleration means the acceleration vector points in the chosen negative direction; it does not automatically mean the object is slowing down.

Formula / representation

SI unit: $m s^{- 2}$
Dimensions: ${LT}^{- 2}$
On a $v$ - $t$ graph: acceleration is gradient.
An object speeds up when velocity and acceleration have the same sign, and slows down when their signs differ.

Common misconceptions

Treating negative acceleration as always meaning deceleration.
Confusing acceleration with velocity or with change in position.
Using $a = \frac{Δ v}{Δ} t$ without keeping a consistent sign convention.
Assuming zero velocity implies zero acceleration; at the top of a vertical flight, velocity is momentarily zero while acceleration remains downward.

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