physicsGrade 11-122 min read

Kinematics: the equations of motion

The four equations for constant acceleration — what each one is for, when to reach for it, and the one decision that picks the right equation every time.

These four equations describe any object moving with constant acceleration (a ball in free fall, a car braking evenly, a trolley down a ramp). Learn what each is for and you'll never have to guess which to use.

The symbols

Symbol	Meaning	Unit
$u$	initial velocity	m/s
$v$	final velocity	m/s
$a$	acceleration	m/s²
$t$	time	s
$s$	displacement	m

The four equations

v = u + at

s = ut + \tfrac{1}{2}at^2

v^2 = u^2 + 2as

s = \left(\frac{u + v}{2}\right)t

How to pick the right one

Every problem gives you three quantities and asks for a fourth. List what you know, then choose the equation that contains your three knowns and your one unknown — and nothing else.

No $s$ in the question? → use $v = u + at$ .
No $t$ in the question? → use $v^2 = u^2 + 2as$ .
No $a$ in the question? → use $s = \left(\frac{u+v}{2}\right)t$ .

Worked example

A car starts from rest and accelerates at $3\ \text{m/s}^2$ for $5\ \text{s}$ . How far does it travel?

Knowns: $u = 0$ , $a = 3$ , $t = 5$ . Unknown: $s$ . No $v$ involved → second equation:

s = ut + \tfrac{1}{2}at^2 = 0 + \tfrac{1}{2}(3)(5)^2 = 37.5\ \text{m}.

Exam tip: write the "known / unknown" list before touching an equation. It turns a panicky search into a one-line decision.

Last revised 10 May 2026.