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# 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*}