# Average Acceleration Formula

Acceleration is defined as the rate of change of velocity. It is denoted by ‘a’ and is measured in the units of m/s2. For a particular interval, the average acceleration is defined as the change in velocity for that particular interval. Unlike acceleration, the average acceleration is calculated for a given interval.

Formula:

Average acceleration is calculated by the following formula,

$Average\,Acceleration = \Delta{v}/\Delta{t}$

Here, Δ v is the change in velocity and Δ t is the total time over which the velocity is changing.

$Average Acceleration = v_{f} – v_{i}/ t_{f} – t_{i}$

where,
vf is the final velocity
vi is the initial velocity
ti is the initial time
tf is the final time

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

$Average\,Acceleration = v_{1}+ v_{2}+ v_{3}+…..+v_{n}/ t_{1}+ t_{2}+ t_{3}+….+t_{n}$

Real-Life Example

If the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s2. Meaning that the marble’s velocity will go up by 20 cm/s each second.

Average acceleration Problems

Example 1: A bus accelerates with an initial velocity of 10 m/s for 5s then 20m/s for 4s finally for 15 m/s for 8s. What can be said about the average acceleration of the bus?
Solution:

It is given that, the velocities of the bus at different time intervals is, v1 = 10 m/s, v2 = 20m/s, v3 = 15m/s
The time intervals for which the object possesses these velocities are t1 = 5s, t2 = 4s, t3 = 8s
Hence, over the interval, the total velocity can be given as the sum of these velocities.

$\Delta v = 10+20+15=45 \frac{m}{s}$

Similarly, the total time interval can be given as the sum of these intervals,

$\Delta t = t _{1}+ t_{2}+ t_{3}= 5+4+8 = 17s$

Using the above formula for average acceleration, we get,

m

$Average\,Acceleration = \Delta {v}/\Delta{t}$

$Average\,acceleration = \frac{45}{17} = 2.65 \frac{m}{s^{2}}$

Question 2: A sparrow, while going back to its nest accelerates to 6 m/s from 3 m/s in 5s. What can we say about its average acceleration?
Solution:

Given: The initial velocity ,vi = 3m/s

The final velocity, vf = 6m/s
Total time for which the acceleration takes place, t = 5 s

$Average Acceleration = v_{f} – v_{i}/ t_{f} – t_{i}$

$Average acceleration = \frac{6-3}{5} = 0.6 \frac{m}{s^{2}}$