Final Velocity Calculator (v = u + at)
This final velocity calculator solves the first equation of motion, v = u + at, one of the four SUVAT equations describing movement under constant acceleration. Rather than only calculating final velocity, it lets you solve for whichever quantity you are missing, final velocity, initial velocity, acceleration or time. Enter the three values you already know into the final velocity, initial velocity, acceleration and time fields, choose the unknown from the solve for dropdown, and the calculator rearranges the formula for you rather than you doing the algebra by hand. It returns the value of the variable solved for in its correct SI unit, alongside a plain summary showing exactly what was calculated, for example final velocity equals 6 m/s. All inputs use standard SI units, velocities in metres per second, acceleration in metres per second squared and time in seconds, so convert imperial or other measurements before entering your figures. This makes it useful for physics students checking homework, teachers building examples, and anyone working through mechanics problems involving constant acceleration, from a dropped ball to a car pulling away from a stop sign. Keep in mind that v = u + at only holds when acceleration is genuinely constant over the interval measured. If acceleration changes during the motion, you will need calculus based methods, or should break the problem into shorter constant acceleration segments instead.
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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