Kinematics Solver
From initial velocity, acceleration, and time, get final velocity and displacement.
Displacement (s): 44.145 m
With constant acceleration, use v = u + at and s = ut + ½at². For an object dropped from rest (u = 0) for t = 3 s at a = 9.81 m/s², the final velocity is 0 + 9.81 × 3 = 29.43 m/s and it falls 44.145 m.
The equations of motion
When acceleration is constant, motion is fully described by five quantities — collectively called SUVAT. Knowing any three of them lets you solve for the rest. This tool starts from initial velocity (u), acceleration (a), and time (t), then gives you the final velocity and displacement. To find the force behind that acceleration, pair it with the force calculator (F = ma).
u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement
Worked example
An object dropped from rest (u = 0) falls for t = 3 s with a = 9.81 m/s²:
- 1 Find the final velocity. v = u + at = 0 + 9.81 × 3 = 29.43 m/s.
- 2 Set up the displacement equation. s = ut + ½at² = 0 × 3 + ½ × 9.81 × 3² = 0 + ½ × 9.81 × 9.
- 3 Compute the displacement. ½ × 9.81 × 9 = 44.145 m fallen in those 3 seconds.
The five SUVAT variables
Pick a consistent positive direction; all five share the same SI units below.
| Symbol | Quantity | SI unit |
|---|---|---|
| s | Displacement | metre (m) |
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | second (s) |
Sign conventions and assumptions
Choose a positive direction and keep it. If you call “up” positive, then gravity is a = −9.81 m/s². A deceleration is simply a negative acceleration — there is no separate equation for it.
Acceleration must be constant. The SUVAT equations break down the moment acceleration changes mid-motion; for that you need calculus or piecewise segments.
Common mistake: forgetting to square the time in ½at². Squaring before multiplying is what makes displacement grow so quickly as time passes.