Deriving Kinematic Equations (Cambridge (CIE) AS Physics)

Deriving kinematic equations of motion

• 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