Average Acceleration: If the velocity of an object changes, it is said to be. Moving with an acceleration.

The time rate of change of velocity of a body is called acceleration.

As velocity is a vector so an change in velocity may be due to change in its magnitude or a change in its direction or both.

Consider a body whose velocity v1 at any instant t changes to v2 in further small time interval ∆t. the two velocity vectors v1 and v2 and the change in velocity, v2 – v1 = ∆ v, are represented in fig. 3.3. the average acceleration equation during time interval ∆t is given by

equation_accelaration

the_two_velocity_vectors

Fig. 3.3

As equation is the difference of two vectors divided by a scalar ∆t, equation must also be a vector. Its direction is the same as that of ∆v. acceleration of a body at a particular instant is known as instantaneous acceleration and it is the value obtained from the average acceleration as ∆t is made smaller and smaller till it approaches zero. Mathematically. It is expressed as

Instantaneous acceleration equation_accelaration_02

If the velocity of a body is increasing, its acceleration is positive but if the velocity is decreasing the acceleration is negative. If the velocity of the body changes by equal amount in equal intervals of time, the body is said to have uniform acceleration. For a body moving with uniform acceleration, its average acceleration is equal to instantaneous acceleration.