Kinematics Calculator — Constant Acceleration
Calculate final velocity, displacement and total distance under constant acceleration, including a direction reversal and a time-by-time table.
Follow a moving object from its initial velocity through a period of constant acceleration. The result separates signed displacement from the total distance travelled, which matters when the object stops and reverses direction. A table samples the motion over the entered interval so the velocity and position changes can be checked together.
How to use this tool
- Choose metres or feet; time is always in seconds.
- Enter initial velocity with its direction sign.
- Enter the constant acceleration in the same length system.
- Enter a nonnegative elapsed time and read the final velocity, displacement and distance.
Formula
v = u + at; displacement = (u + v)t/2; distance = the sum of the magnitudes travelled before and after any reversal
u is initial velocity, a is acceleration, t is elapsed time and v is final velocity. If −u/a lies strictly inside the interval, velocity changes sign there. Splitting the path at that instant prevents cancellation of distance travelled in opposite directions.
Example
An object starts at 10 m/s with acceleration −2 m/s² for 8 s. It stops after 5 s, having moved 25 m forward, then moves 9 m backward. Final velocity is −6 m/s, displacement is 16 m, and total distance is 34 m.
Frequently asked questions
Does negative acceleration always slow an object?
No. An acceleration opposite to velocity reduces speed; one with the same sign increases speed. A negative acceleration speeds up motion that is already negative.
Why can distance exceed displacement?
Displacement compares start and end positions. Distance adds every part of the path, including travel after a reversal.
What happens at zero time?
Position has not changed and final velocity equals initial velocity. A time average over an interval of zero duration is undefined and is shown as such.
Can this model drag or changing acceleration?
Only if the constant-acceleration assumption is appropriate. This tool does not integrate a time-varying force or a multidimensional trajectory.
Sources
Last updated: 2026-10-30