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# Acceleration

## Acceleration definition

Acceleration is the rate of change of velocity with respect to time.

An object accelerates when its velocity (i.e. its direction or its speed) changes over time.

In everyday language, 'acceleration' means an increase in speed. In physics, acceleration is any kind of change in velocity.

An increase in speed, a reduction in speed and change in direction are all accelerations.

You can feel acceleration but not velocity.

You can feel acceleration when a car changes its speed. If you move at a constant velocity, you cannot feel the motion.

A plane that is landing is also accelerating, but its acceleration is negative.

## Acceleration main formula

Like displacement $(s)$ and velocity $(v)$, the acceleration $(a)$ is a vector quantity.

Often we use the symbols $\Tred{u}$ for initial velocity, $\Tblue{v}$ for final velocity and $\Delta v$ for change in velocity.

If the velocity and acceleration are in the same direction, the magnitude of acceleration $\Torange{a}$ can be calculated using:

\begin{align*}\Torange{\text{acceleration}}&=\frac{\Tblue{\text{final velocity}}-\Tred{\text{initial velocity}}}{\text{time}} \\ \Torange{a} & = \frac{\Tblue{v}-\Tred{u}}{t} = \frac{\Delta v}{t}\end{align*}

The unit of acceleration is metres per second squared $(\text{m/s}^2)$. This is equal to the unit of velocity $(\text{m/s})$ divided by the unit of time $(\text{s})$: $$\frac{\text{m/s}}{\text{s}}=\frac{\text{m}}{\text{s}^2} = \text{m/s}^{2} = \text{m s}^{-2}$$

The average velocity during constant acceleration $a$ along a straight line is:\begin{align*}\text{average velocity}=&\frac{\Tred{\text{initial velocity}} + \Tblue{\text{final velocity}}}{2} \\ v_{avg}=& \frac{\Tred{u} +\Tblue{v}}{2} \end{align*}