# 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 t1 and  t2 is the velocity at time t2 minus the velocity at time t1 divided by Δt = t2 – t1. The unit of acceleration is m/sand it can be larger than 0, equal to 0 or small than 0.

$${ \overline { a } }_{ { t }_{ 1 },{ t }_{ 2 } }=\frac { { v }_{ { t }_{ 2 } }-{ v }_{ { t }_{ 1 } } }{ { t }_{ 2 }-{ t }_{ 1 } }$$

In the figure, instantaneous velocity is 0 at the start (at P1) and it begins to increase because the slope of the tangent line increases. From t1 to t2, the average acceleration is larger than 0.

$${ \overline { a } }_{ { t }_{ 1 },{ t }_{ 2 } }>0$$

However, if you take the acceleration between t1 and t5, that is smaller than 0. At time t1, the velocity is 0 and at time t5, 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 v2 minus v1 divided by impact time ∆t.

$${ \overline { a } }=\frac { 5-(-5) }{ { 10 }^{ -2 } } ={ 10 }^{ 3 }\frac { m }{ { s }^{ 2 } }$$
Instead of tennis ball, if an egg hit the floor with 5 m/s, it will not come back and break. Therefore the change of velocity will not be 10 m/s but it will only be 5 m/s. The impact time would be probably longer. The acceleration during the impact is lower. Something breaks because magnitude of acceleration becomes too high.