Equations of Motion (SUVAT)

The SUVAT equations apply when an object moves with constant (uniform) acceleration in a straight line.

Symbol	Quantity	Unit
$s$	displacement	m
$u$	initial velocity	m/s
$v$	final velocity	m/s
$a$	acceleration	m/s$^2$
$t$	time	s

The four equations are:

$v = u + at$

$s = \frac{(u + v)}{2} \times t$

$s = ut + \frac{1}{2}at^2$

$v^2 = u^2 + 2as$

Each equation links four of the five SUVAT variables. To solve a problem, identify the three known values and one unknown, then select the equation that contains all four.

Worked example: A car accelerates from rest ($u = 0$) at 2.5 m/s$^2$ for 8 s. Find the distance.

$s = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}(2.5)(8^2) = 80\text{ m}$

Common errors and how to correct them

• Using SUVAT when acceleration is not constant (e.g. during braking with variable friction).
• Forgetting that $u = 0$ for objects starting from rest.
• Mixing up $u$ and $v$ when the object is decelerating.

How to apply this in an exam

Write the SUVAT list first. Fill in every known value, identify the unknown, then pick the equation that contains exactly those four quantities. Show the substitution clearly.