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Kinematics is the branch of physics that describes motion — how objects move through space over time — without worrying about the forces that cause that motion. The SUVAT equations are the five fundamental relationships that connect displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) under constant acceleration.
The four core SUVAT equations are: v = u + at (velocity-time), s = ut + ½at² (displacement-time), v² = u² + 2as (velocity-displacement), and s = ½(u+v)t (average velocity). Given any three of the five variables, you can always find the remaining two.
These equations apply directly to everyday motion problems: a car braking to a stop, a ball thrown upward, or an aircraft accelerating down a runway. They assume constant acceleration — if acceleration varies, calculus (integration) is needed instead.
Worked example: A car accelerates from rest (u = 0) at a = 3 m/s² for t = 5 s. Using v = u + at: v = 0 + 3×5 = 15 m/s. Using s = ut + ½at²: s = 0 + ½×3×25 = 37.5 m.
v = u + at | s = ut + ½at² | v² = u² + 2as
Enter any 3 of the 5 variables. Leave 2 blank to solve.
SUVAT Equations Reference
| Equation | Missing Variable | Use When |
|---|---|---|
| v = u + at | s (displacement) | You know u, a, t |
| s = ut + ½at² | v (final velocity) | You know u, a, t |
| v² = u² + 2as | t (time) | You know u, a, s |
| s = ½(u+v)t | a (acceleration) | You know u, v, t |
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.