Dynamics, Kinematics & Vibrations

a = dv/dt = d²s/dt². Also a = v(dv/ds), the velocity form used when acceleration is given as a function of position.

v² = v₀² + 2a(s − s₀). It eliminates time and is valid only when acceleration a is constant.

s = s₀ + v₀t + ½at². Valid only for constant a; the ½at² term is the contribution of acceleration over time t.

Displacement. The area under a v–t curve between two times equals the change in position; the slope of the v–t curve is acceleration.

Tangential aₜ = dv/dt (change in speed) and normal aₙ = v²/ρ (change in direction), where ρ is the radius of curvature. Normal points toward the center of curvature.