**AVERAGE ACCELERATION FORMULA AND EXAMPLE**

## Average Acceleration Formula

Average acceleration is the quantity that measures a change in velocity over a particular time interval. Formula for average acceleration is change of velocity divided by time elapsed.

In symbols, the average acceleration between time t_{1} and t_{2} is the velocity at time t_{2} minus the velocity at time t_{1} divided by Δt = t_{2} – t_{1.} The unit of acceleration is m/s^{2 }and it can be larger than 0, equal to 0 or small than 0.

In the figure, instantaneous velocity is 0 at the start (at P_{1}) and it begins to increase because the slope of the tangent line increases. From t_{1} to t_{2}, the average acceleration is larger than 0.

However, if you take the acceleration between t_{1} and t_{5}, that is smaller than 0. At time t_{1}, the velocity is 0 and at time t_{5}, the velocity is negative so if we substitute these numbers in the average acceleration formula, we will get a minus average acceleration.

So signs in velocity and acceleration depend on how the positive direction of motion is defined. If the positive direction of motion is reversed, all the signs will change.

Average acceleration formula can also be stated as below.

\({ \overline { a } }=\frac { \Delta v }{ \Delta t } \)## Average Acceleration Example

Let’s assume that a tennis ball hits the floor with -5 m/s velocity and bounce back with a velocity of 5 m/s as shown below.

The average acceleration is v_{2} minus v_{1} divided by impact time ∆t.