4.5.5—Instantaneous acceleration

Acceleration is dv/dt, the instantaneous rate of change of velocity. Since velocity is ds/dt, acceleration is d²s/dt².

Keep signs and units consistent, and distinguish average acceleration Δv/Δt from the derivative at one instant.

If v(t)=t²−4t, then a(t)=2t−4; at t=3 the acceleration is 2 m s⁻².

Zero velocity does not imply zero acceleration: an object can be momentarily at rest while its velocity changes.