Motion, momentum & energy
Start with the model and its assumptions. These relationships use SI units unless you convert every quantity consistently.
Motion, momentum & energy
| Relationship | Formula | When it applies |
|---|---|---|
| Average motion | vavg = Δr/Δt; average speed = distance/Δt | Distance is path length; displacement is change in position. |
| Constant acceleration | v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx | Apply per component only when that acceleration is constant. |
| Projectile motion | x = v₀ cos θ · t; y = y₀ + v₀ sin θ · t − ½gt² | Uniform downward gravity, negligible air resistance. |
| Gravitation | F = GMm/r²; U = −GMm/r | Outside a spherically symmetric source or for point masses; r is centre-to-centre separation and U = 0 at infinity. |
| Momentum & impulse | p = mv; J = ∫F dt = Δp | Total momentum is conserved when net external impulse is zero. |
| Work & kinetic energy | W = ∫F · dr; K = ½mv²; Wnet = ΔK | Classical nonrelativistic motion. |
| Potential energy & power | Ug = mgh; Us = ½kx²; P = dW/dt = F · v | mgh assumes nearly uniform gravity; x is spring deformation. |
Find definitions and the original reference tables in the glossary →