Equations of motion Equations and definitions

For one-dimensional motion with constant acceleration:

Symbol	Meaning
$s$	displacement from initial position
$u$	initial Velocity
$v$	final Velocity
$a$	constant acceleration
$t$	elapsed time

SUVAT equations

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

Choosing an equation

Pick the equation that leaves out the variable you do not know and do not need. Example: if time is not given, $v^2=u^2+2as$ is often the cleanest choice.

Vector warning

These scalar equations assume motion along one chosen axis. Choose a positive direction first, then give $u$, $v$, $a$, and $s$ signs relative to that axis.

Related: Kinematic, Equations of motion Examples, Equations of motion Common pitfalls.

Initial position convention

These equations usually take initial position as zero, so $s$ is displacement rather than absolute position. If the object starts at $x_0$, write $x=x_0+s$. For example, $x=x_0+ut+\frac{1}{2}a{t}^2$ is the position form of the second SUVAT equation.