Deriving the suvat Formulae (Edexcel International A Level (IAL) Maths: Mechanics 1): Revision Note

Deriving the suvat Formulae

What is suvat?

• suvat is an acronym for the five quantities used when modelling motion in a straight-line with constant acceleration

  • s – displacement (from the starting point)

  • u – initial velocity

  • v – final velocity

  • a – acceleration

  • t – time

• All except time are vector quantities and can be negative

  • time is a scalar quantity

What are the suvat (constant acceleration) equations?

• The five equations for motion in a straight line are:

$\begin{array}{l}v=u+at\\ v^2=u^2+2as\\ s=\frac{1}{2}(u+v)t\\ s=ut+\frac{1}{2}a{t}^2\\ s=vt-\frac{1}{2}a{t}^2\end{array}$

• The equations can only be used when the motion has constant acceleration

• All equations connect four of the five quantities

  • Knowing any three allows a fourth to be found

• The equations are not provided in the exam so you need to memorise them

How do I derive the suvat equations?

• The four equations that involve time can be derived from a velocity-time graph

  • The velocity-time graph will be a straight line as the acceleration is constant

  • The fifth equation can be found by choosing any two of the equations and eliminating the t variable (see the worked example)