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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:$$$\begin{align*}\text{average velocity}=&\frac{\Tred{\text{initial velocity}} + \Tblue{\text{final velocity}}}{2} \\ v_{avg}=& \frac{\Tred{u} +\Tblue{v}}{2} \end{align*}$$$