Motion Equations Solver

Enter any three of displacement, initial and final velocity, acceleration and time to get the other two, with working.

Runs entirely in your browser. Nothing you type or paste is sent anywhere.

What you know

DisplacementHow far it ends up from the start

Initial velocityVelocity at the start

Final velocityVelocity at the end

AccelerationRate of change of velocity

TimeHow long it takes

3 of 5 filled in. Finding s and v.

Examples

Answer

Displacement

s =36m

Final velocity

v =13m/s(46.8 km/h)

The shaded area under the line is the displacement: ½ × (u + v) × t = 36 m. Area below the time axis counts as negative.

Working

Find v using v = u + at

v = u + at

v = 5 + 2 × 4

v = 13 m/s

Find s using s = ut + ½at²

s = ut + ½at²

s = 5 × 4 + ½ × 2 × 4²

s = 36 m

The five equations

v = u + atno sUsed
s = ut + ½at²no vUsed
s = vt − ½at²no u
v² = u² + 2asno t
s = ½(u + v)tno a

Signs matter

Choose one direction as positive. Anything pointing the other way is negative: for a ball thrown upwards with up as positive, a = −9.8 m/s². These equations assume the acceleration stays the same the whole time.

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