Mechanics

g (gravitational field strength)

g = 9.81 N kg^-1

speed (with time)

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

v=\dfrac{d}{t}

velocity

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

\bm{v}=\dfrac{\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}=\dfrac{\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\dfrac{\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}

gravitational potential energy

gpe (J) = mass (kg) × gravitational field strength (N kg^-1) × height (m)

E_{grav}=m\bm{g}h

E_{grav}=m\bm{g}\Delta h

kinetic energy

kinetic energy (J) = ½ × mass (kg) × (speed)² (m²s^-2)

E_{k}=\frac{1}{2}mv^2 

speed (after falling a certain distance from rest)

v=\sqrt{2\bm{g}\Delta h}

how high an object could rise if projected upwards at a certain speed

\Delta h = \dfrac{v^2}{2\bm{g}}

work done

work done (J) = force (N) × distance moved in direction of force (m)

\Delta W = \bm{F}\Delta\bm{s}

work done by a force at an angle

\Delta W = \bm{F}\Delta \bm{s}\cos\theta

power

power (W) = energy transferred (J) / time for the energy transfer (s)

P=\dfrac{E}{t} 

power (W) = work done (J) / time for the work to be done (s)

P=\dfrac{\Delta W}{t} 
power (W) = [force (N) × distance moved (m)] / time for the force to move (s)
P=\dfrac{\bm{F}\Delta \bm{s}}{t} 

efficiency

efficiency = useful work done / total energy input

momentum

momentum (kg m s^-1) = mass (kg) × velocity (m s^-1)

\bm{p} = m \times \bm{v} 

applied force

applied force (N) = change in momentum (kg m s^-1) / time (s)

\bm{F} = \dfrac{\text{d}\bm{p}}{\text{d}t} = \dfrac{\text{d}(m\bm{v})}{\text{d}t} 

\bm{F} = \dfrac{\Delta\bm{p}}{\Delta t}