# Advanced Knowledge of Acceleration

Physics

## definition

### Acceleration

Acceleration is defined as the rate of change of velocity with time. It is a vector quantity. Its unit is
Constant speed does not guarantee that acceleration is zero. For example a body moving with constant speed in a circle changes its velocity every instant and hence its acceleration is not equal to zero.

## definition

### Retardation

Retardation (or deceleration) of a body whose velocity is decreasing with time is defined as the negative of acceleration. In other words, it is equal to the magnitude of acceleration of a body whose velocity is decreasing with time.
For a decelerating body, direction of velocity and acceleration is always opposite in direction.
Example: When a body is thrown vertically upwards, during the upward motion, its velocity decreases and at the highest point it becomes zero. This is a case of retardation.

## formula

### Understand Acceleration as Second Derivative of Displacement

Where is a displacement vector.

## formula

### Definition of Jerk

Rate of change of acceleration is defined as jerk.
jerk =

## definition

### Acceleration as a rate of change of velocity with respect to displacement

Acceleration is defined as

Example:

If the velocity of a particle is given by , then find its acceleration.

Solution:

Differentiate both sides w.r.t , we get: