• Acceleration

The rate of change in velocity is called acceleration. Acceleration is generally denoted by a or f. Thus, for one dimensional motion,

Acceleration = Change in velocity / Time taken

⇒ a = (Final velocity - Initial velocity) / Time taken in change in velocity

⇒ a = (v −u) / t

Where, ‘a’ is acceleration, ‘v’ is final velocity, ‘u’ is initial velocity and ‘t’ is time taken for change.

A positive sign of acceleration shows increase in velocity and a negative sign show decrease in velocity. If there is decrease in velocity, it is called retardation. This means, rate of decrease in velocity is called retardation.

Note:

1. Acceleration is a vector quantity.
2. Its is the same as the direction of velocity of the body.
3. It can be either positive, zero or negative.
4. Acceleration of a body is zero when it moves with uniform velocity.
5. It is measured in cm/s2 in cgs system of units, m/s2 in SI system of units and km/h2 in practical life when distance and time involved are large.

In the case of uniform velocity, the speed or direction of a moving object is not changed and thus there is no change in acceleration. Therefore, in the case of uniform velocity acceleration will be zero.

Uniform Acceleration: A body is said to be moving with uniform acceleration, if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time. or A body has uniform acceleration if its velocity changes at a uniform rate. For examples, the motion of a freely falling body and the motion of a sliding block on a smooth  inclined plane are uniformly accelerated motion.

Non-uniform Acceleration: A body is said to be moving with non-uniform acceleration, if its velocity increases by unequal amounts in equal intervals of time. A body has non-uniform acceleration if its velocity changes at a non-uniform rate. For examples, The motion of a car on a crowded city road.  Its speed (velocity) changes continuously.