How this instrument works
SUVAT is shorthand for the five quantities that describe motion under constant acceleration: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Classic kinematics teaching pairs them into five equations, each one omitting a different variable, so that any three known quantities determine the other two. This instrument takes the three easiest to measure directly — initial velocity, acceleration, and time — and returns the pair that needs no substitution: final velocity from v = u + at, and displacement from s = ut + ½at². Neither formula depends on the other's result, which is why they are the pair worth computing first.
Both equations fall out of the same starting point. Acceleration is defined as the rate velocity changes, a = (v − u) ⁄ t, and rearranging that definition gives v = u + at with no integration needed. Displacement follows from the shape of a velocity-time graph: under constant acceleration, velocity rises in a straight line from u to v, so the average velocity across the interval is exactly (u + v) ⁄ 2. Multiply that average by t and substitute v = u + at in place of v, and the terms rearrange themselves into s = ut + ½at² — no separate derivation required, just algebra on a definition.
The constant-acceleration assumption is doing real work, and it fails wherever the force driving the motion is not steady. A skydiver in freefall does not follow s = ut + ½at² for long, because air resistance grows with speed and the net acceleration shrinks toward zero as terminal velocity approaches. SUVAT is exact for a single steady force — something dropped in a vacuum, a vehicle braking on a surface with a genuinely constant friction coefficient — and only approximate anywhere acceleration itself changes during the interval.
- Enter Initial velocity in m/s — use 0 for an object starting from rest, such as a weight released with no push.
- Enter Acceleration in m/s²; use 9.80665 for free fall under standard gravity, or a negative value for something slowing down.
- Enter Time in seconds — the duration over which that acceleration acts without changing.
- Read Final velocity, the speed at the end of the interval, computed from v = u + at.
- Read Displacement, the net distance covered over that same interval, computed from s = ut + ½at².
Worked example — a weight dropped for 3 seconds
Release a weight from rest, so Initial velocity u = 0 m/s, and let gravity alone act on it, Acceleration a = 9.80665 m/s², for a Time of t = 3 s. The first equation gives Final velocity directly: v = 0 + 9.80665 × 3 = 29.41995 m/s, just over 105 km/h reached from a standing start in three seconds of unresisted fall.
The second equation gives how far it fell: s = (0 × 3) + ½ × 9.80665 × 3² = ½ × 9.80665 × 9 = 44.129925 m, roughly a fourteen-storey drop covered in that same three seconds. Neither figure depends on the weight's mass — a coin and a wrench released together under these numbers would still be falling side by side, both reading 29.42 m/s, because mass appears in neither equation.
Questions
What does the acronym SUVAT stand for?
Displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) — the five variables of one-dimensional motion under constant acceleration. Textbook kinematics gives five equations, each omitting exactly one of the five; this calculator solves the two that need no substitution, v = u + at and s = ut + ½at².
Why does the calculator only need three inputs to find two answers?
Because final velocity and displacement each follow directly from initial velocity, acceleration, and time without needing the other unknown first. v = u + at never references s, and s = ut + ½at² never references v, so both come out of one pass through the same three numbers — no simultaneous equations, no iteration.
Can I use this if the acceleration is not constant?
No — both formulas assume a stays fixed for the whole interval. Air resistance, changing engine thrust, or friction that grows with speed all break that assumption, and the results only describe the motion approximately, if at all. For genuinely variable acceleration, the correct approach integrates a(t) directly rather than plugging into these two shortcuts.
What if the object is slowing down rather than speeding up?
Enter a negative value for Acceleration. A car braking at 4 m/s² from 20 m/s, for instance, uses a = −4 to find how far it travels before stopping. The same two formulas handle slowing down and speeding up identically — the sign of a does the work, so there is no separate mode to switch to.
Where do the SUVAT equations actually come from?
Straight from the definition of constant acceleration, a = (v − u) / t, rearranged to v = u + at, plus the geometry of a velocity-time graph: under constant acceleration, velocity rises in a straight line, so displacement equals the average velocity, (u + v)/2, multiplied by time. Substituting v = u + at into that average produces s = ut + ½at².
Does the result change with the object's mass?
No. Both equations use only velocity, acceleration, and time — mass never appears in either. A heavier and a lighter object released with the same initial velocity and acceleration reach the same final velocity and cover the same displacement in the same time, the counterintuitive result Galileo is credited with demonstrating against the older assumption that heavier objects fall faster.