Calculators
Kinematics Calculator
Solve one-dimensional constant-acceleration motion problems.
Kinematics Calculator tool
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About This Tool
Kinematics describes motion without needing to model the forces that cause it. For straight-line motion with constant acceleration, a small set of equations connects initial velocity u, final velocity v, acceleration a, elapsed time t, and displacement s. This calculator handles common three-known-value workflows while keeping units and direction signs explicit.
How To Use It
- Choose the motion quantity to calculate.
- Enter the three requested values in SI units: meters, seconds, meters per second, and meters per second squared.
- Choose one positive direction before entering values. Velocity, acceleration, and displacement may be negative when they point opposite that direction.
- Check that acceleration can reasonably be treated as constant across the interval before applying the result.
Examples
Accelerating vehicle
Starting at 5 m/s with constant acceleration 2 m/s² for 10 s gives v = u + at = 25 m/s and s = ut + ½at² = 150 m.
Braking
If a vehicle travels at 20 m/s and acceleration is −2 m/s² for 5 s, its final velocity is 10 m/s. The negative acceleration indicates it acts opposite the chosen positive direction.
Find acceleration
Changing velocity from 4 m/s to 16 m/s in 6 s gives a = (v − u)/t = 2 m/s².
Useful Notes
Core equations
For constant acceleration, v = u + at and s = ut + ½at² are two common time-based equations. Another useful relation is v² = u² + 2as when elapsed time is not known.
Direction and negative values
Signs carry physical meaning. Pick a positive axis first. Motion or acceleration opposite that axis is negative; a negative velocity does not automatically mean an object is slowing down.
Displacement is not distance
Displacement is the signed change in position. Total distance traveled is always non-negative and can differ from displacement if the object reverses direction.
Constant acceleration assumption
The equations on this page require acceleration to remain constant during the modeled interval. Variable acceleration generally requires piecewise analysis, calculus, numerical methods, or measured motion data.
Units
The interface uses SI units so the equations remain consistent: meters for displacement, seconds for time, m/s for velocity, and m/s² for acceleration. Convert other units before entering them.
Physical interpretation
A mathematically valid result still depends on a physically appropriate model. Reaction time, drag, road grade, changing thrust, collisions, and other effects can make a simple constant-acceleration calculation unsuitable for real-world prediction.
FAQ
What are the SUVAT variables?
They commonly represent displacement s, initial velocity u, final velocity v, acceleration a, and time t.
Can acceleration be negative?
Yes. A negative sign means acceleration points opposite your chosen positive direction. Whether that slows the object depends on the velocity direction.
Can initial velocity be negative?
Yes. It means the initial motion is opposite the direction you defined as positive.
Is displacement the same as distance?
No. Displacement is signed position change; distance is total path length and cannot be negative.
When should I not use these equations?
Do not treat them as exact when acceleration varies materially over the interval unless you divide the motion into segments where constant acceleration is a reasonable approximation.