# Average Acceleration and its formula & solved numerical problems

When velocity changes an object is said to undergo acceleration. Quantitatively, we define acceleration as the rate of change of velocity, just as we defined velocity as the rate of change of position. The average acceleration over a time interval Δt is the ratio of change in velocity Δv (that takes place over the time interval Δt) and the time interval Δt itself.

where Δv is the change in velocity over the time interval Δt.
And the bar on a indicates that this is an average value.

## How to find the average acceleration with formula

– For a time duration Δt, we have to get the initial and final velocity.
– Then we have to find out the difference between the final velocity and initial velocity. Use this one to do that,
Δv = Vfinal –  Vinitial
– Now, we have to calculate the ratio of Δv and Δt. [ as we know, a = Δv / Δt ]
– This will give us the average acceleration value.
If you find the value negative that means it’s actually retardation.

## Sample numerical problems on average acceleration – all solved

1 ) A car is moving with a velocity of 20 m/s. The driver accelerated it for 10 seconds and reached a velocity of 40 m/s. What is the average acceleration?

Solution:
Initial velocity = 20 m/s and final velocity is 40 m/s.

And the elapsed time = 10 seconds

Therefore, a = Δv / Δt = (40 -20) / 10 m/s^2 = 2 m/s^2

2 ) A car is moving with a velocity of 30 m/s. The driver applied brake for 5 seconds to bring it down to zero. What is the average acceleration? Is it retardation?

Solution:
Initial velocity =30 m/s and final velocity is 0 m/s.

And the elapsed time = 5 seconds

Therefore, a = Δv / Δt = (0-30) / 5 m/s^2 = -6 m/s^2

The negative value of a tells that it’s actually retardation.