Final Velocity (Uniform Acceleration)

Also known as first kinematic equation · v = v₀ + at · SUVAT v = u + at

v = v_0 + a t

Worked example: Car merging: 15 m/s + 2 m/s² for 5 s → 25 m/s — press Try an example to run it live, then adjust anything.

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Final Velocity (Uniform Acceleration) explained

Under constant acceleration, velocity changes at a steady rate, so the final speed is simply the starting speed plus the acceleration multiplied by the elapsed time. Picture a car merging onto a highway: entering the ramp at 15 m/s and holding a steady 2 m/s² for 5 seconds, it reaches v = 15 + (2)(5) = 25 m/s — right at highway pace. Deceleration works the same way with a negative a, which is how stopping times are estimated from braking data.

This is the first of the SUVAT equations, the toolkit of uniformly accelerated motion that traces back to Galileo's inclined-plane experiments in the early 1600s, where he showed that falling bodies gain equal speed in equal times. Because the relationship is linear in every variable, each of the four rearrangements has exactly one answer — no square roots, no ambiguity — making it the friendliest member of the kinematics family.

Final Velocity (Uniform Acceleration) formula

v = v_0 + a t

Where

$v$ = Final velocity (m/s)
$v_0$ = Initial velocity (m/s)
$a$ = Acceleration (m/s²)
$t$ = Time (s)

Missing one of these? Work it out first, then come back

Final velocity — Velocity-Displacement Relation (v² = v₀² + 2ad), Displacement from Average Velocity
Initial velocity — Displacement (Uniform Acceleration), Velocity-Displacement Relation (v² = v₀² + 2ad)
Acceleration — Newton's Second Law, Displacement (Uniform Acceleration)
Time — Speed, Distance & Time, Displacement from Average Velocity

Part of this formula set

The kinematic equations

5 formulasThe five equations of motion under constant acceleration, and the trick for choosing between them: pick the one missing the quantity you neither have nor want.