Average Acceleration Formula

Average acceleration formula is the change in the velocity divided by the time interval. And the formula for the same is, the average acceleration formula = (change in velocity)/(time taken). Acceleration or average acceleration is measured in m/s².

In this article, we will learn about, Average Acceleration Definition, Average Acceleration Formula, its Examples and others in detail.

What is Average Acceleration?

Average acceleration calculates the changes in velocity over time. We quantify the ratio of the change in velocity as the velocity is divided over the elapsed time to find the average acceleration of any object. We can simply say that the average acceleration is the change in velocity divided by the time taken for that change to take place. Mathematically, average acceleration ([Tex]\vec{a}[/Tex]) is represented as:

[Tex]\vec{a}[/Tex] = Δv/Δt

​where,

• Δv is Change in Velocity
• Δt is Time Interval

Average Acceleration Formula

Formula for average acceleration is given as:

a = (v_f – v_i)/t

where,

• v_f is Final velocity
• v_i is Initial velocity
• t is Time Interval

Also if, object shows different velocities, i.e. v₁, v₂, v₃…v_n for different time intervals such as t₁, t₂, t₃…t_n respectively, the average acceleration is calculated using the following formula,

Average Acceleration = (v₁ + v₂ + v₃ + … + v_n)/(t₁ + t₂ + t₃ + … + t_n)

Unit of Average Acceleration

Unit of average acceleration is similar to the unit of acceleration and the unit of acceleration is m/s², cm/s², etc.

How to Derive Average Acceleration?

Acceleration formula can be easily found using integral method that includes:

a = dv/dt

Here dv is change in velocity, and dt is change in time. Integrating both sides of this equation, we get:

[Tex]\int_{v_{i}}^{v_{f}} adv~=~\int_{0}^{t}dt[/Tex]

Solving the integrals, we get

v_f – v_i = at

Rearranging terms yields the average acceleration formula:

a = (v_f – v_i)/t

This can be explained using the example added below as:

Find average acceleration from 0 sec to 6 sec

Time (Seconds)	Velocity (m/s)
0	0
2	20
4	40
6	60

Solution:

• V_{(at 6 sec)} = 60 m/s
• V_{(at 0 sec)} = 0 m/s
• t = (6 – 0) sec = 6 sec

Average Acceleration(a) = {V_{(at 6 sec)} – V_{(at 6 sec)}}/t

a = (60 – 0)/6

a = 60/6 = 10 sec

Example on Average Acceleration Formula

Example 1: Kabir bought a new car which can get off 0 to 60 m/s in 7 seconds only. Estimate the average acceleration of the car.

Solution:

Given:

• Final Velocity v_f = 60 m/s
• Initial Velocity v_i = 0
• Time(Δt) = 7 sec

A_avg = Δv/Δt

A_avg = 60/7

A_avg = 12.86 m/s²

Therefore, the acceleration of the car is 12.86 m/s².

Example 2: A bus driver is driving on a narrow path at 14 m/s and is about to hit a pup that is running across the street. Therefore, the bus gradually started slowing down from the speed of 3 m/s while taking 1.5 sec to do so. Calculate the bus acceleration.

Solution:

Given:

• v_f = 3 m/s
• v_i = 45 m/s

A_avg = Δv / Δt

A_avg = (3 – 45) / 1.5

A_avg = (- 42) / 1.5

A_avg = – 28 m/s²

Acceleration of the bus is -28 m/s². Here, negative sign signifies speeding up of the object.

FAQs on Average Acceleration

What is average acceleration class 11?

Average acceleration refers to the rate change of velocity over a fixed period of time.

What is SI unit of average acceleration?

SI unit of average acceleration is meters per second per second or simply meters per second squared (m/s²).

Can acceleration be negative?

Yes, acceleration can be negative. An object with reducing velocity have negative acceleration.

How does average acceleration differ from instantaneous acceleration?

Average acceleration refers to the overall speed-change over a time period, whereas instantaneous acceleration means the acceleration at a certain moment of time.