**Average acceleration:** The average acceleration of an object is its change in velocity divided by the time required for that change. For instance, if the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s/s. This means that the marble’s velocity will increase by 20 cm/s every second.

**Explanation:** Suppose the velocity of a body at time t_{0} is v_{0}^{→} and at later time t the velocity is v^{→}. Here change of time is t – t_{0} = ∆t and change of velocity is v^{→} – v_{0}^{→} = ∆v. So, according to definition the average acceleration of the body.

a^{→} = (v^{→} – v_{0}^{→}) / (t – t_{0}) = ∆v/∆t

For one dimensional motion along X-axis, average acceleration will be,

a_{x}^{→} = ∆v_{x}/∆t î; and its magnitude is,

a_{x} = ∆v_{x}/∆t.

**Example:** A car accelerates with an initial velocity of 10 m/s for 5s then 20 m/s for 4s finally for 15 m/s for 8s. Calculate the average acceleration?

Solution:

Given: Velocity v_{1} = 10 m/s, v_{2} = 20m/s, v_{3} = 15m/s

Time taken t_{1} = 5s, t_{2} = 4s, t_{3} = 8s

Total velocity Δ v = v_{1} + v_{2} + v_{3} = 10 + 20 + 15 = 45 m/s

Total time taken Δ t = t_{1} + t_{2} + t_{3} = 5 + 4 + 8 = 17 s

The average acceleration is given by a = Δv/Δt = 45/17 = 2.647 ms^{-2}