Deriving the suvat Equations (OCR A Level Maths: Mechanics)

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 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

Use the constant acceleration equations

and 

to show that

.