Mechanics

speed

speed (m s^-1) = distance (m) / time (s)

v=\frac{d}{t}

velocity

velocity (m s^-1) = displacement (m) / time (s)

\bm{v}=\frac{\Delta\bm{s}}{\Delta t}

acceleration

acceleration (m s^-2) = change in velocity (m s^-1) / time taken to change the velocity (s)

\bm{a}=\frac{\Delta\bm{v}}{\Delta t}

moment of a force

moment (Nm) = force (N) × perpendicular distance from the pivot to the line of action of the force (m)

moment = \bm{F}x

resultant force needed to give an acceleration

resultant force (N) = mass (kg) × acceleration (m s^-2)

\sum\bm{F}=m\bm{a}

final velocity

final velocity (m s^-1) = initial velocity (m s^-1) + acceleration (m s^-2) × time (s)

\bm{v}=\bm{u}+\bm{a}t

displacement (with final velocity)

displacement (m) = time (s) × (initial velocity (m s^-1) + final velocity (m s^-1)) / 2

\bm{s}=t\times\frac{\bm{u}+\bm{v}}{2}

displacement (with acceleration)

displacement (m) = initial velocity (m s^-1) × time (s) + ½ × acceleration (m s^-2) × time (s)²

\bm{s}=\bm{u}t + \frac{1}{2}\bm{a}t^{2} 

final velocity² (with displacement)

final velocity (m s^-1)² = initial velocity (m s^-1)² + 2 × acceleration (m s^-2) × displacement (m)

\bm{v}^{2}=\bm{u}^{2}+2\bm{as}