Kinematics Calculator
Find final velocity, displacement and average velocity from initial velocity, acceleration and time.
How it works
v = u + a·t and s = u·t + ½·a·t²
These are the constant-acceleration equations of motion. Given a starting velocity, a steady acceleration and a time interval, the first equation gives the final velocity and the second gives the distance travelled. The average velocity is simply the mean of the start and end speeds.
Worked example
Dropped from rest (u = 0) under gravity (a = 9.81 m/s²) for 3 s: v = 0 + 9.81 × 3 = 29.42 m/s, and s = 0 + ½ × 9.81 × 3² = 44.13 m.
Frequently asked questions
Do these equations always work?
They assume acceleration is constant over the time interval. For changing acceleration you need calculus or to break the motion into segments with different constant accelerations.
What sign should acceleration have?
Pick a positive direction and keep it consistent. Deceleration or gravity opposing the motion is entered as a negative acceleration.
How do I model free fall?
Set initial velocity to 0 and acceleration to 9.80665 m/s² (standard gravity). Displacement is then the distance fallen.
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Educational estimate. Check the formula and units for your exact case.