Deriving the suvat Formulas (OCR AS Maths A: Mechanics): Revision Note

Deriving the suvat equations

What does suvat stand for?

• 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 equations for constant acceleration?

• The five suvat 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 provided in the exam

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)

  
  

• Two of the equations can also be derived using calculus

  • Velocity is found by integrating acceleration

  • Displacement is found by integrating velocity