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Motion (kinematics) cheat sheet

All 6 formulas on one page. Print it or save it as a PDF; it fits on 2 sides of A4 or Letter.

Speed, distance and time

v = d/t

Distance

d = vt

Time

t = d/v

$v$ the average speed (m/s in the calculator)
$d$ the distance travelled (m)
$t$ the time taken (s)

Final velocity: v = u + at

v = u + at

$v$ the final velocity in m/s
$u$ the initial velocity in m/s
$a$ the acceleration in m/s², assumed constant; negative if it acts against the positive direction (g = 9.81 m/s² for free fall)
$t$ the time in seconds

Displacement: s = ut + ½at²

s = ut + 1/2at²

$s$ the displacement in metres: distance in a chosen positive direction (it can be negative)
$u$ the initial velocity in m/s
$a$ the acceleration in m/s², assumed constant; negative if it acts against the positive direction (g = 9.81 m/s² for free fall)
$t$ the time in seconds

Velocity and displacement: v² = u² + 2as

v² = u² + 2as

$v$ the final velocity in m/s
$u$ the initial velocity in m/s
$a$ the acceleration in m/s², assumed constant; negative if it acts against the positive direction (g = 9.81 m/s² for free fall)
$s$ the displacement in metres: distance in a chosen positive direction (it can be negative)

Displacement from average velocity

s = (u + v)/2 t

$s$ the displacement in metres: distance in a chosen positive direction (it can be negative)
$u$ the initial velocity in m/s
$v$ the final velocity in m/s
$t$ the time in seconds

Projectile range

R = (v²sin 2θ)/g

Maximum height

H = (v²sin ²θ)/(2g)

Time of flight

T = (2vsin θ)/g

$R$ the horizontal range in metres (it lands at the height it was launched from)
$v$ the launch speed in m/s
$θ$ the launch angle above the horizontal, between 0° and 90°
$g$ the acceleration due to gravity, 9.81 m/s² on Earth

letx.io · Motion (kinematics) cheat sheet · 2026-10-31