Average Acceleration Formula

Acceleration is defined as the rate of change of velocity. It is denoted by â€˜aâ€™ 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.Â Unlike acceleration, the average acceleration is calculated for a given interval.

Formula:

Average acceleration is calculated by the following formula,

$$\begin{array}{l}Average\,Acceleration = \Delta{v}/\Delta{t}\end{array}$$

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

$$\begin{array}{l}Average Acceleration = v_{f} – v_{i}/ t_{f} – t_{i}\end{array}$$

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, v3â€¦vn for different time intervals such as t1, t2, t3â€¦t3 respectively, the average acceleration is calculated using the following formula,

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

Real-Life Example

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

Average acceleration Problems

ExampleÂ 1:Â 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, v1Â = 10 m/s, v2Â = 20m/s, v3Â = 15m/s
The time intervals for which the object possesses these velocities are t1Â = 5s, t2Â = 4s, t3Â = 8s
Hence, over the interval, the total velocity can be given as the sum of these velocities.

$$\begin{array}{l}\Delta v = 10+20+15=45 \frac{m}{s}\end{array}$$

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

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

Using the above formula for average acceleration, we get,

m

$$\begin{array}{l}Average\,Acceleration = \Delta {v}/\Delta{t}\end{array}$$

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

QuestionÂ 2:Â 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 ,viÂ = 3m/s

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

$$\begin{array}{l}Average Acceleration = v_{f} – v_{i}/ t_{f} – t_{i}\end{array}$$

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