SUVAT (constant acceleration)

Five kinematics equations linking displacement (s), initial velocity (u), final velocity (v), acceleration (a), time (t).

Y12 Mechanics. Five equations: v = u + at; s = ut + ½at²; v² = u² + 2as; s = (u+v)t/2; s = vt − ½at². Each connects four of the five variables.

Worked examples

Stone dropped: u = 0, a = g = 9.8 m/s². After 3 s: v = 29.4 m/s; s = 44.1 m.

Car decelerating: u = 30 m/s, a = −5, t = 4: v = 10 m/s, s = 80 m.

Stopping distance from 30 m/s, deceleration 7.5 m/s²: v²=0 ⇒ s = 60 m.

Frequently asked questions

Constant acceleration only?

Yes — that's a SUVAT condition. Variable acceleration uses calculus methods.

Take care with signs?

Pick a positive direction; keep all quantities consistent. Up positive, gravity negative (or vice versa).