Displacement s, initial velocity u, final velocity v, acceleration a, time t. Each equation omits one, so with any three known you can reach the other two.
Look at the two quantities you were not given, decide which you want, and use the equation that omits the other. Faster than rearranging.
Constant acceleration. The velocity–time graph is a straight line, and every equation is its endpoint, gradient or area. When the line bends, all five stop being true.
A quadratic for time and a square root for velocity each have two roots, and both are real motions. A calculator that returns one has chosen for you.
s is how far you ended up from where you started along your chosen positive direction. A ball thrown straight up and caught again has s = 0 though it travelled several metres; if it lands in a well below you, s is negative. No SUVAT equation gives distance travelled directly.
Drag grows roughly with the square of speed, so a falling object’s acceleration drops steadily toward zero at terminal velocity. Over a short fall the error is small; over a long one SUVAT confidently overestimates: a skydiver reaches about 53 m/s and stays there, where SUVAT predicts 98 m/s after ten seconds. A dropped feather, a long fall, a cyclist coasting: no SUVAT equation applies. See the Galileo drop simulator.
Whatever your chosen positive direction says. If up is positive, gravity is a = −9.81 m/s², a ball thrown up starts with positive u, and braking gives a negative a while the car still moves forwards. Mixing conventions halfway through is the commonest way these problems go wrong.
The defined standard value is 9.80665, used here. Actual local gravity varies from about 9.78 at the equator to 9.83 at the poles: a 0.5% spread, which matters more than the difference between 9.81 and 9.80665 for anything you are likely to measure.
Because there genuinely are two. Throw a ball upward at 20 m/s and ask when it is 15 m high: it passes that height at 0.99 s on the way up and again at 3.09 s on the way down, moving at the same speed in opposite directions. Solving for time uses a quadratic, and solving for a velocity takes a square root — both have two roots, and both roots are real motions. A calculator that silently returns one of them has picked for you without saying so.
That you finished on the negative side of where you started. s is displacement, not distance travelled. A ball thrown up that lands back in your hand has s = 0 even though it has covered several metres — and if it lands in a well below you, s is negative.
Whatever your chosen positive direction says. Pick one — up, or forwards — and every quantity takes its sign from that choice. If up is positive then gravity is a = −9.81 m/s², a ball thrown up starts with positive u, and braking gives a negative a while the car still moves forwards. Mixing conventions halfway through is the single most common way these problems go wrong.
Almost always air resistance, which SUVAT does not contain. A dropped feather, a long fall, a cyclist coasting — all of them have a force that grows with speed, so the acceleration is not constant and no SUVAT equation applies. The rule of thumb is that it holds well for dense objects over short falls, and starts to mislead beyond a few seconds of free fall. For a fall with real drag, see the Galileo drop simulator.
This page has changed in 174 archived releases, but each of those was a site-wide pass, so none is attributable to this tool on its own and none is listed here. That is not a claim that the tool never changed — a release that reworked many pages at once may well have altered this one too. The changelog has them.