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 is
When
its velocity is
When
the displacement is 2m. Find expressions in terms of
for the velocity and displacement.
When
When
Example:
The displacement of a particle is
Find 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 when
is
The acceleration whenis