About the Kinematics (SUVAT) Calculator
This kinematics calculator solves constant-acceleration motion problems using the five SUVAT equations. Choose which three of the five quantities you know — displacement s, initial velocity u, final velocity v, acceleration a and time t — enter them, and it finds the remaining two, shows which equation it used and plots position and velocity over time.
It is built for GCSE, A-level, AP and first-year university physics, and for practical questions such as how far a car travels while braking, how long a runway a plane needs, or how fast a cyclist is going at the bottom of a hill. All ten possible combinations of three known values are supported.
Values use SI units — metres, metres per second, metres per second squared and seconds — and signs matter: pick a positive direction and give opposite quantities negative values (for example, braking is a negative acceleration). The equations only apply when acceleration is constant.
How to use the kinematics (suvat) calculator
- 1Choose the combination of three values you know.
- 2Enter them in SI units, using negative signs for motion or acceleration in the opposite direction.
- 3Read the two solved quantities and the equations used.
- 4Check the chart to see how displacement and velocity change over time.
Formula and method
For motion in a straight line with constant acceleration, five quantities are linked by the SUVAT equations. Each equation leaves out one of the five variables, so with any three known values you can pick the equation that omits the unknown you do not need, solve for one unknown, then use another equation for the last one.
When a square root is involved (v² = u² + 2as) the calculator takes the root that gives a non-negative time. Signs follow the direction you choose as positive; a negative acceleration means slowing down if the object moves in the positive direction. Air resistance or any changing force breaks the constant-acceleration assumption.
- s
- Displacement (m)
- u
- Initial velocity (m/s)
- v
- Final velocity (m/s)
- a
- Constant acceleration (m/s²)
- t
- Time elapsed (s)
Worked examples
Car accelerating from rest
Starting at rest with a = 3 m/s² for 5 s: v = 0 + 3 × 5 = 15 m/s and s = ½ × 3 × 5² = 37.5 m.
Braking distance
A car at 25 m/s (90 km/h) braking at 6 m/s² stops in t = 25 ÷ 6 ≈ 4.17 s and travels s = (0 − 625) ÷ (2 × −6) ≈ 52.1 m.
Speed after rolling down a slope
v² = 2² + 2 × 1.5 × 50 = 154, so v ≈ 12.41 m/s, and t = (12.41 − 2) ÷ 1.5 ≈ 6.94 s.
Acceleration from distance and time
From rest, 100 m in 10 s needs a = 2 × 100 ÷ 10² = 2 m/s², reaching v = 2 × 100 ÷ 10 − 0 = 20 m/s.
Frequently asked questions
What does SUVAT stand for?+
SUVAT lists the five variables of constant-acceleration motion: s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time). The equations are named after them.
How many values do I need to solve a kinematics problem?+
You need three of the five SUVAT quantities. Each equation involves four of them, so three knowns let you find a fourth, and then the fifth follows from another equation.
When can I use the SUVAT equations?+
Only when acceleration is constant and motion is in a straight line (or treated one direction at a time, as in projectile motion). Changing forces such as air drag or a spring require calculus or numerical methods.
Why is my acceleration negative?+
A negative acceleration means it points opposite to your chosen positive direction. If the object is moving in the positive direction, that means it is slowing down, as in braking.
What is the difference between displacement and distance?+
Displacement is the straight-line change in position including direction; distance is the total path length. A ball thrown up and caught has zero displacement but has travelled a distance.