Kinematics calculator
Choose what to find, enter the initial velocity u and the two other known values. The calculator applies the equations of uniformly accelerated motion (SUVAT) and also gives the one remaining quantity and the average speed.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: final velocity, displacement, acceleration or time.
- Enter the initial velocity u and the two values the form asks for, in m/s, m/s², s and m.
- Read the answer, the other quantity it gives and the average velocity.
- Final velocity: v = u + a·t, and s = u·t + ½·a·t².
- Displacement: s = (u + v) × t ÷ 2, and a = (v − u) ÷ t.
- Acceleration: a = (v² − u²) ÷ (2s), and t = 2s ÷ (u + v).
- Time: the first t > 0 with u·t + ½·a·t² = s: t = (−u + √(u² + 2as)) ÷ a, or s ÷ u when a = 0.
Worked example
A cart starts from rest and accelerates at 2 m/s² for 5 s: v = 0 + 2 × 5 = 10 m/s, and it covers s = ½ × 2 × 5² = 25 m, an average of 5 m/s.
A runner at 5 m/s speeds up at 2 m/s². How long to cover 24 m? 24 = 5t + t², so t = (−5 + √(25 + 96)) ÷ 2 = 3 s, and the final speed is 5 + 2 × 3 = 11 m/s.
Tips and common mistakes
- Constant acceleration only. If the acceleration changes, split the motion into stages and use the final velocity of one stage as u of the next.
- Convert units first. 72 km/h is 20 m/s (divide by 3.6).
- Displacement is not distance. For a ball that goes up and comes back down, s is the change in position and can be zero or negative.
Frequently asked questions
What are the SUVAT equations?
Five equations for motion in a straight line with constant acceleration, named after their letters: s displacement, u initial velocity, v final velocity, a acceleration, t time. v = u + at, s = ut + ½at², s = (u + v)t ÷ 2, v² = u² + 2as and s = vt − ½at². Each one leaves out one quantity.
How do I enter braking or motion upwards?
Pick one direction as positive and give every quantity a sign. A car braking from 20 m/s has a negative acceleration, for example −4 m/s². A ball thrown upwards with u = 15 m/s has a = −9.81 m/s² if up is positive.
Why does it say there is no solution?
The motion never reaches that displacement. A car braking from 10 m/s at −2 m/s² stops after 25 m, so it can never cover 30 m in the same direction. The time must also come out positive.
Can I use this for free fall?
Yes. Use a = 9.81 m/s² (or −9.81 with up as positive) and ignore air resistance. The free fall calculator does the same for a dropped object with heights and impact speed.