Deriving the suvat Formulae (Edexcel IAL Maths)

Spec point — 3.1

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:

$v=u+at\,v^{2}=u^{2}+2as\,s=\frac{1}{2}(u+v)t\,s=ut+\frac{1}{2}at^{2}\,s=vt-\frac{1}{2}at^{2}$

• 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)

Worked Example Use the constant acceleration equations

s = $\frac{1}{2}$(u+v)t and v = u + at

to show that

v² = u² + 2as.

Answer:

Exam Hint

• If asked to derive any of the formulae there may be a velocity-time graph provided. Make sure you show each step and state any reasons such as the gradient of the graph being the acceleration.
• If the question does not ask you to derive the formulae then you can use them freely without proof.