2.6 Acceleration
Whenever the velocity of an object is increasing, we say that the object is accelerating. For example, when a car overtakes another one, it accelerates to a greater velocity. On the contrary, the velocity decreases when brakes are applied to slow down a bicycle or a car. In both cases, a change in velocity occurs.
Acceleration is defined as the time rate of change of velocity.
The change in velocity can occur in magnitude or direction or both. The acceleration is positive if the velocity is increasing and negative if the velocity is decreasing. Negative acceleration is also called deceleration or retardation.
Acceleration is a vector quantity like velocity, but the direction of acceleration is that of the change of velocity. If a body is moving with an initial velocity v_i and after some time t its velocity changes to v_f, the change in velocity is Δv = v_f − v_i that occurs in time t. In this case, the rate of change of velocity, i.e., acceleration, will be the average acceleration.
Average acceleration = Change in velocity / Time taken
a_av = (v_f − v_i) / t
This can also be written as:
a_av = Δv / t
The SI unit of acceleration is m s⁻².
If acceleration a is constant, then the equation can be written as:
v_f = v_i + at