Two formulas cover most problems
If speed is steady, velocity is just distance over time. If the object accelerates at a constant rate, the kinematic equations relate starting velocity, acceleration, time and distance. Pick the one that has the value you are missing.
Here v is final velocity, u is initial velocity, a is acceleration, t is time and d is distance.
Solving for whichever value is missing
Each equation rearranges to give any one of its variables. These are the forms the solver uses under the hood.
- From v = u + at. Time: t = (v − u) ÷ a. Acceleration: a = (v − u) ÷ t.
- From v² = u² + 2ad. Distance: d = (v² − u²) ÷ 2a. Acceleration: a = (v² − u²) ÷ 2d.
- When u² + 2ad is negative there is no real answer — the object stops before it covers that distance.
Worked example: braking car
- Setup. A car enters a curve at u = 20 m/s and brakes at a = −4 m/s² for t = 3 s.
- Final velocity. v = 20 + (−4 × 3) = 8 m/s.
- Distance covered. d = (8² − 20²) ÷ (2 × −4) = (64 − 400) ÷ (−8) = 42 m.
Speed unit conversions
| m/s | km/h | mph | ft/s | knots |
|---|---|---|---|---|
| 1 | 3.6 | 2.24 | 3.28 | 1.94 |
| 5 | 18 | 11.2 | 16.4 | 9.72 |
| 10 | 36 | 22.4 | 32.8 | 19.4 |
| 30 | 108 | 67.1 | 98.4 | 58.3 |
| 100 | 360 | 223.7 | 328.1 | 194.4 |
| 343 | 1235 | 767.3 | 1125 | 667.0 |
343 m/s is the speed of sound in air at 20°C. Quick mental check: 100 km/h ≈ 62 mph ≈ 28 m/s ≈ 54 knots.
Where these formulas break down
- Constant acceleration only. The kinematic equations assume a steady rate. If acceleration changes, they no longer hold.
- Average, not instantaneous. Using v = d/t on an accelerating object gives the average velocity over the trip, not the speed at any one instant.
- Keep units consistent. Do not mix kilometers with seconds — convert everything to one system first.
Common questions
How do you calculate velocity?
For steady motion, divide distance by time: v = d divided by t. If the object is speeding up or slowing down at a constant rate, use v = u + at, where u is the starting velocity, a is acceleration and t is time.
What is the difference between speed and velocity?
Speed is just how fast something moves. Velocity is speed with a direction attached, so it can be negative. A car doing 60 km/h north has a velocity; 60 km/h on its own is a speed.
How do I convert m/s to km/h?
Multiply by 3.6. So 10 m/s is 36 km/h. Going the other way, divide by 3.6.
