A particle moving with *variable velocity* is said to possess acceleration. When a particle executes non-uniform motion, its velocity changes. *Acceleration* is defined as the *rate of change of velocity*. It is a vector quantity. The *unit of acceleration* is cm s^{-2} in G.G.S. system and metre per second per second (m s^{-2}) in S.I systems.

By definition, acceleration, a¯ = change in velocity/Time = v¯-u‾/t

Example

A car moves along a straight path with variable velocity as shown in the figure. When the car is at position A, its velocity is 10 m s^{−1} and when it is at position B, its velocity is 20 m s^{−1}^{.} If the car takes 5 seconds of time to move from A to B, find the acceleration of the car.

Solution

Initial position of the car at position A = u = 10 m s^{−1}

Final velocity of the car at position B = v = 20 m s^{−1}

The change in velocity of the car, Δv = v = 20 m s^{−1 } −10m s^{−1} = 10 m s^{−1}

The time taken for the car to move from A to B, Δt = 5 s

∴ Acceleration of the car, a = Δv/Δt = 10 m s^{−1} = 2 m s^{-2}.

## Uniform Acceleration

If the change in velocity of the body is equal in an equal interval of time then the body is said to move with *uniform acceleration*.

## Acceleration Due to Gravity

Objects thrown vertically upwards move up to a certain distance and then fall back to the ground. This is due to the earth’s gravitational force.

Due to gravitational force, all objects are accelerated towards the Earth. This uniform acceleration towards the Earth, irrespective of the mass is known as *acceleration due to gravity *and is denoted by ‘g’.

Equations of Motion of Objects under the Influence of Gravity ( Neglecting air Resistance )

Here, since acceleration of a body moving vertically, either upward or downward, is due to gravity, ‘a’ is substituted by ‘g’ and the displacement ‘s’ is substituted by ‘h’. Thus, we have

v = u+gt

s = ut+½ gt^{2}

v^{2 }= u^{2} + 2gh

Where,

v is the final velocity,

u is initial velocity,

g is *acceleration due to gravity* and t is time taken.

‘g’ is chosen to be positive if the body is moving towards the Earth, i.e., downward and g is negative if the body is moving in upwards direction.

NOTE , It is purely a matter of choice and convenience that we choose a particular direction as positive. In the above case, for example, the final result will remain the same even if we choose the upward direction as positive and downward as negative or vice—versa.