## Acceleration

When the velocity of a moving body changes, we are usually interested how fast (or how slow) it changes. “The measure of change in velocity with the passage of time is called acceleration”. Mathematically,

Where is the final and is the initial velocity of the body.  Δt refers to the elapsed time and equal to the difference in final time tf and initial time ti. As   is a vector, acceleration is also a vector quantity.

Units of acceleration are ms-2 and its dimensions are |L1T-2|.

As velocity is a vector quantity, the change in velocity may be due to a change in the magnitude of the velocity or its direction.

• If the magnitude of the velocity changes and its direction is constant, the acceleration produced is linear acceleration.
• If the magnitude of the velocity is constant and the direction changes, the acceleration produced is centripetal or radial acceleration.

Similarly, if the velocity increases with time, the acceleration is positive. If the velocity of the body decreases, the acceleration is negative.

### Types of acceleration

Depending upon the changes, there are certain types of acceleration.

#### Average Acceleration

Average acceleration is defined as the net velocity divided by the total time taken.

#### Instantaneous Acceleration

Acceleration at a particular interval of time is called instantaneous acceleration.

If the time Δt is made smaller and smaller such that it approaches zero, the average acceleration approaches instantaneous acceleration. Mathematically,

#### Uniform Acceleration

If the velocity of a body changes by equal amounts in equal intervals of time, the body is said to have uniform acceleration. Average and instantaneous accelerations are equal when the body is moving with uniform acceleration.

#### Variable Acceleration

A body is said to be moving with variable acceleration if its velocity changes by unequal amounts in equal intervals of time.