# Average Acceleration Formula

Last updated on June 2nd, 2023 at 09:09 am

In this post, we have taken the **Average Acceleration Formula **as our topic of discussion. We will see how to define and find it, and how to solve sample numerical problems using the formula. This post is useful for **class 11** students who are studying this chapter.

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.

**Definition** of **Average Acceleration**

**The average acceleration over a time interval Δ t is the ratio of change in velocity Δv (that takes place over the time interval Δt) and the time interval Δt itself.**

**Average Acceleration Formula**

Average Acceleration

a_{avg}=Δ/vΔt

where Δvis the change in velocity over the time interval Δt.

Also Read about **Instantaneous Acceleration – formula, definition, numerical problems**

How to find average acceleration with the 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 the initial velocity. Use this one to do that,

Δv = V_{final} – V_{initial}

– Now, we have to calculate the ratio of Δv and Δt. [ as we know, **a**_{avg} = 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.

**Also Read:** (suggested reading)

Difference between Instantaneous Speed and Instantaneous Velocity

Difference between average speed and average velocity

Instantaneous Velocity – definition & equation with solved problem

Average velocity – definition, formula

Instantaneous Acceleration – definition & formula with solved problem

Average Acceleration and its formula & solved numerical problems