How this calculator works
- Step 1Velocityv = u + a tChanges by a every second.
- Step 2Distances = u t + ½ a t²Area under the velocity line.
- Step 3Stoppingu² ÷ 2|a|When braking to rest.
With steady acceleration, velocity changes by the same amount each second. The distance covered is the average velocity times the time.
Signs show direction. A negative acceleration against a positive velocity is braking, and the calculator also gives how long and how far it takes to stop.
Worked example: braking from 20 m/s
- v
u + a t- s
u t + ½ a t²
- Final velocity20 − 4 × 38.00 m/s
- Displacement20 × 3 − ½ × 4 × 3²42.00 m
- Time to stop20 ÷ 45.00 s
- Stopping distance20² ÷ (2 × 4)50.00 m
Read the result
A car at 100 km/h braking hard at 7 m/s² needs 55.11 m to stop, before adding reaction time.
- Displacementwith directionCan be negative or less than distance travelled.
- Speedwithout directionThe size of the velocity.
Assumptions and limits
- Constant aAcceleration does not change.
- Straight lineOne dimension; use projectile motion for arcs.
- No reaction timeBraking starts at t = 0.
- Past the stopEquations assume it then reverses.
Related motion tools
Constant acceleration in a line is the base case. Two directions and energy build on it.
For a thrown or launched object, use the projectile motion calculator. The kinetic energy calculator gives the energy at any speed, and the speed calculator handles average speed.
Common mistakes
Mistake: Using a positive a for braking.
Instead: Give acceleration the opposite sign to velocity.
Mistake: Entering km/h.
Instead: Divide by 3.6 for m/s.
Checking the method
A separate script steps every motion forward in tiny time steps, without the closed-form equations, and matches each golden value.
Read how we test our calculators, or browse more maths calculators.