The relationship between displacement, velocity and acceleration is summarised in the following diagram.

Given the displacement, to find the velocity, we differentiate. To find the acceleration, we differentiate twice.

Given the acceleration, to find the velocity, we integrate. To find the displacement, we integrate twice.

Example

A particle P moves on the- axis. At time t seconds, its acceleration isWhen its velocity isWhenthe displacement is 2m. Find expressions in terms of for the velocity and displacement.

When

When

Example:

The displacement of a particle isFind the velocity and acceleration in terms of t. When is the particle at rest for? What are the displacement and acceleration at this time?

When the particle is at rest,

The particle is at rest whenor

The displacement whenis

The acceleration whenis