# Acceleration, average Acceleration, uniform Acceleration, variable Acceleration, instantaneous Acceleration

Acceleration: The state of change of velocity of a body with time is known as its acceleration.

If the velocity of a body increases with time, then its acceleration is positive. On the other hand, if the velocity of a body decreases with time, then its acceleration is negative. Negative acceleration is also called retardation or deceleration. Acceleration is a vector quantity.

Units of acceleration. The units of acceleration are:

Cms-2 in the CGS system

And                                          ms-2 in the MKS system or SI units

Average Acceleration. When a body is moving with variable acceleration, then its average acceleration in a given interval of time is defined as the ratio of the change in velocity of the body to the time interval.

If v1 is the velocity of the body at time t1 and v2 is the velocity of the body at time t2, then its average acceleration during the time interval (t2 – t1) is given by.

a = v2 – v1/t2 – t1

Uniform Acceleration. A body is said to be moving with uniform acc. if its average acc. between any two points along its path is the same in magnitude as well as direction.

Or

A body is said to be moving h uniform acceleration if its velocity changes by equal amounts in equal intervals of time, however small these intervals may be.

Variable Acceleration. A body is said to be moving with variable acceleration if its average acceleration is different between different points along its path, either in magnitude or in direction or both in magnitude as well as direction.

Or

A body is said to be moving with variable acceleration if its velocity changes by unequal amount in equal intervals of time, however small these intervals may be.

Instantaneous Acceleration. When a body is moving with variable acceleration, then its acceleration at a particular instant of time or at a particular position along its path is known as its instantaneous acceleration It is equal to the limiting value of average acceleration as Dt tends to zero, which shows that the instantaneous accelration of a body is equal to the first derivative of velocity or the second derivative of displacement w.r.t time.