Average Acceleration — Formula, Definition and Unit

The formula for average acceleration is:

Average Acceleration (a) = Change in Velocity / Time taken

Mathematically written as: a = (v − u) / t
or a = Δv / Δt

Where:

• a = Average acceleration
• v = Final velocity
• u = Initial velocity
• t = Time taken for the change (Δt)
• Δv = Change in velocity (v - u)

• Velocity is measured in metres per second (m/s).
• Time is measured in seconds (s).
• Therefore, Acceleration is measured in metres per second squared (m/s²).

• Positive Acceleration: If final velocity (v) is greater than initial velocity (u), the acceleration is positive. This means the object is speeding up.
• Negative Acceleration (Deceleration/Retardation): If final velocity (v) is less than initial velocity (u), the acceleration is negative. This means the object is slowing down.
• Zero Acceleration: If v = u, the velocity is constant. The object is neither speeding up nor slowing down.

Question: A car moving at 10 m/s accelerates steadily and reaches a speed of 30 m/s in 5 seconds. What is its average acceleration?

Solution:

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 30 m/s
• Time (t) = 5 s

Formula: a = (v − u) / t a = (30 − 10) / 5 a = 20 / 5 a = 4 m/s²

The car's average acceleration is 4 m/s².