Differentiation for Kinematics
How is differentiation used in kinematics?
- Displacement, velocity and acceleration are related by calculus
- In terms of differentiation and derivatives
- velocity is the rate of change of displacement
- or
- acceleration is the rate of change of velocity
- or
- so acceleration is also the second derivative of displacement
- or
- velocity is the rate of change of displacement
Worked example
The displacement, m, of a particle at seconds, is modelled by the function .
Find expressions for and , and state what these expressions represent.
means the same as
This expression represents the velocity of the particle.
Answers may or may not need to be factorised, depending on the question
means the same as
This expression represents the acceleration of the particle.