Deriving Kinematic Equations (CIE AS Physics)

• The kinematic equations of motion are a set of four equations which can describe any object moving with constant acceleration
• They relate the five variables:
  • s = displacement
  • u = initial velocity
  • v = final velocity
  • a = acceleration
  • t = time interval

• It’s important to know where these equations come from and how they are derived:

Deriving v = u + at

A graph showing how the velocity of an object varies with time

Deriving s = (u + v)t

The average velocity is halfway between u and v

 

Deriving s = ut + at²

The two terms ut and ½at² make up the area under the graph

Deriving v² = u² + 2as

This final equation can be derived from two of the others

Summary of the equations of motion

Summary of the four equations of uniformly accelerated motion