Average Acceleration Formula

The rate of change of velocity is defined as acceleration. It is denoted by 'a' and is measured in units of m/s2. For a particular duration, average acceleration for that particular duration is defined as the difference of velocity during that particular duration. In contrast to acceleration, average acceleration is calculated for a definite interval.

Formula

Average acceleration is defined by the following formula, 

Average Acceleration = Δ v / Δ t

Here,

• Δv is the change in velocity and 

• Δt is the total time over which the velocity is changing. 

Average Acceleration = vf - vi / tf - ti

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 is having different velocities say v1, v2, v3…vn for different intervals of time as t1, t2, t3…tn respectively then the average acceleration can be calculated by using the following formula:

Average Acceleration = v1+ v2+ v3+...+vn /  t1 +  t2 + t3 +…+ t3

Real-Life Example

If the velocity of a marble is increased from 0 to 60 cm/s in 3 seconds, then the average acceleration would be 20 cm/s2. That means the velocity of the marble would increase by 20 cm/s every second.

Solved Problems

Problem 1: A bus accelerates from 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 span for which the object has these velocities are t1 = 5s, t2 = 4s, t3 = 8s

Thus, for the span of time, the net velocity can be expressed as the sum of these velocities.

 

Similarly, the net span of time can be expressed as the sum of these spans,

Using the above expression for average acceleration, we have,

Problem 2: A sparrow, reurns to his nest accelerates to 6 m/s from 3 m/s in 5s. What can be said about his 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 = 5s

Conclusion

Understanding average acceleration is very important in kinematics because it would help in describing the way objects move and interact under various forces. Make sure you practice many different kinds of problems so that you will understand how to go about solving problems.

 

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