Deriving the suvat Equations (Edexcel International A Level Maths: Mechanics 1)

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:

• 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)