The SUVAT equations describe motion at constant acceleration: v = u + a·t and s = u·t + ½·a·t². Drag the sliders below to set the initial velocity, acceleration and time, and watch the displacement and final velocity respond in real time.

Fixing u, a and t to pin down where the ball is and how fast it's moving

Set three numbers on this simulator and everything else about the motion follows. The sliders Initial velocity u (m/s), Acceleration a (m/s²) and Time t (s) feed two equations at once: final velocity v = u + a·t tells you how fast the object is moving at that instant, while displacement s = u·t + ½·a·t² tells you where it has ended up. The readouts for s and v update together, so the same three inputs pin down both the position and the speed with no extra bookkeeping.

With the object moving forwards, slide a above zero and it speeds up; drag a below zero and it decelerates, then reverses. Watch the positive/negative-displacement indicator: because s is a vector, it can read negative or even zero. Push u forward against a negative a and you can send the ball out and back so s lands at 0 while it clearly covered ground — displacement is not the distance travelled. Notice too that with a nonzero, s is quadratic in t, so it never grows in a straight line.

One rule holds throughout: these formulas assume constant acceleration. A ball on a smooth ramp or a car braking at a steady rate fit them exactly; a skydiver whose acceleration keeps changing does not. Keep every value in SI units. To crunch specific figures, use the SUVAT calculator, or try a different motion sandbox over in the physics simulation collection.

Frequently asked questions

What are the SUVAT equations?

They describe motion at constant acceleration. This lab uses v = u + a·t and s = u·t + ½·a·t², where s is displacement, u the initial velocity, v the final velocity, a the acceleration and t the time.

When do the SUVAT equations apply?

Only when the acceleration is constant. They fit a ball rolling down a smooth ramp or a car braking at a steady rate, but not motion where the acceleration keeps changing, such as a skydiver whose acceleration falls as drag builds.

Is displacement the same as distance travelled?

No. Displacement is a vector — it can be negative or even zero. An object thrown straight up and returning to its start has zero displacement but has still travelled a real distance.

What does a negative acceleration mean?

A negative acceleration slows an object that is moving forwards, and can then drive it back the other way. Acceleration and displacement both carry a sign that records direction, not just size.

References & formula source

  • Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 2 (Motion Along a Straight Line).
  • Young & Freedman — University Physics with Modern Physics, §2.4 (Motion with Constant Acceleration).
  • R. Nave — HyperPhysics, Georgia State University, "Motion Equations" section.