Average Acceleration Formula

Acceleration is a very familiar term you must have definitely heard of especially relating to cars. When the velocity of an object changes, we say it is accelerating. Thus, acceleration is the rate of change of velocity with time. In layman’s term, we use acceleration to describe a state of increasing speed. Similar to velocity, there are two kinds of acceleration which are average and instantaneous. Average acceleration is determined over a long interval of time. When we use the word long over here, we use it in the context of finite i.e. anything with a beginning and an end. Thus, this article will focus on average acceleration formula.

Definition

Average acceleration refers to the rate at which the velocity changes. We divide the change in velocity by an elapsed time to find out the average acceleration of anything.

For instance, if the velocity of a crazy ball increases from 0 to 60 cm/s in 3 seconds, the average acceleration of the ball would be 20 cm/s/s. Therefore, it means that the velocity of the marble will increase by 20 cm/s every second. The table given below will help you understand better the operation:

Time (Seconds)	Velocity (cm/s)
0	0
1	20
2	40
2	60
4	80

 

Therefore, we see that average acceleration is described as the ratio of change in velocity to the change in time for a specified interval. Contrasting instantaneous acceleration, the average acceleration is calculated for a specified interval.

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Formula

When we talk about acceleration, we see that it is the rate of change for velocity. In other words, it is the change in velocity over a particular period of time. Similarly, the average acceleration is the final velocity minus the initial velocity per time is taken. Therefore, the formula for average acceleration formula is:

A_avg = Δv / Δt

Over here:

A_avg refers to the average acceleration, m/s²

Δv is v_f – v_i, m/s

Δt refers to t_f – t_i, s

Solved Examples for You

Question- Your sister just bought a new car which goes from 0 to 60 m/s in just 7 seconds. Calculate the acceleration of the car.

Answer- First, we will work with what we have. Thus, we have been given the final velocity which is v_f = 60 m/s along with the initial velocity which is v_i = 0. Further, our final time is t_f = 7 sec in addition to the initial time which is t_i = 0. Therefore, when we apply the average acceleration formula, we get:

A_avg = Δv / Δt

A_avg = (60 m/s) / 7 s

A_avg = 12.86 m/s²

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

Question- A bus driver is driving along a side-road at 45 m/s when suddenly he encounters a puppy run across the street. Thus, he rapidly slows down to 3 m/s within a time span of 1.5 sec. Calculate the acceleration of the bus.

Answer- Placing the figures in the equations, we will see that we have our final velocity as v_f = 3 m/s and our initial velocity, v_i = 45 m/s. In addition to the time we have, t = 1.5 sec. Therefore, by applying the average acceleration formula, we will get:

A_avg = Δv / Δt

A_avg = (3 m/s – 45 m/s) / 1.5 sec

A_avg = (- 42 m/s) / 1.5 sec

A_avg = – 28 m/s²

Therefore, the acceleration of the bus is -28 m/s². It is important to note over here that the negative sign indicates the slowing down of the object.