Analysing motion

Equations and graphs

Physics can be described as modelling the natural world using mathematics.

In the case of moving objects, physics can accurately record and even predict the movement of objects using a set of physical laws and equations.

These equations have helped launch space vehicles and are responsible for the realism of many computer games.

Equations of motion

The equations of motion relate to the following five quantities:

  • u - initial velocity
  • v - final velocity
  • a - acceleration
  • t - time
  • s - displacement

A box has an initial velocity u. After time t has elapsed it has a final velocity v and has undergone a displacement s.

Of the above u, v, a, and s are vector quantities. Time (t) is a scalar quantity.

If any three of the five quantities are known then the other two may be calculated using the following four equations:

v = u + at

s = ut + \frac{1}{2}a{t^2}

{v^2}= {u^2} + 2as

s= \frac{{u + v}}{2}t

The equations of motion can only be used for an object travelling in a straight line with a constant acceleration.

Remember to make vectors going in one direction positive and vectors in the opposite direction negative.