Final Velocity Calculator (v = u + at)

This final velocity calculator uses the first equation of motion, v equals u plus at, which links final velocity to initial velocity, constant acceleration and time. Pick which quantity you want and enter the other three; the calculator rearranges the formula and solves for it. This is one of the four SUVAT equations for motion under constant acceleration, the foundation of mechanics at school and first year university. Use SI units: velocities in metres per second, acceleration in metres per second squared and time in seconds. The formula, a worked example and the assumptions are below.

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Final velocity (m/s)

Initial velocity (m/s)

Acceleration (m/s\u00B2)

Time (s)

Solve for

Value

Result

The formula

The first equation of motion is v = u + at, where v is final velocity, u is initial velocity, a is constant acceleration and t is time. Rearranged: u = v minus at, a = (v minus u) / t, and t = (v minus u) / a.

Worked example

Starting from rest (u = 0) with acceleration 2 m/s squared for 3 seconds, the final velocity is v = 0 + 2 times 3 = 6 m/s. Solve for v with u = 0, a = 2, t = 3 to confirm.

Frequently asked questions

What is the formula v = u + at?

The first SUVAT equation: final velocity equals initial velocity plus acceleration times time, for constant acceleration.

Can I solve for time or acceleration?

Yes. Choose the unknown in the dropdown and enter the other three values; the calculator rearranges for you.

Does it assume constant acceleration?

Yes. The SUVAT equations only hold when acceleration is constant over the interval.

Who this calculator is for

This calculator is for physics students, teachers and engineers.

What this calculator assumes

You enter SI units as labelled.
One variable is solved from the others.
Results are rounded for display.

Formula and sources

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Kinetic Energy Calculator: energy of motion.
Momentum Calculator: mass times velocity.
Projectile Motion Calculator: range and height.

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