Calculate signed final velocity from initial velocity, constant acceleration, and either elapsed time or signed displacement. Convert metric or imperial units and inspect later arrivals and stopping diagnostics.

Zero elapsed time returns the initial velocity.

One-dimensional motion with constant acceleration. Velocity, acceleration and displacement are signed; choose one positive direction. Displacement mode shows the earliest nonnegative-time arrival and any later arrival.

Final Velocity Formula

For one-dimensional motion with constant acceleration, the time route uses:

Vf = Vi + a × t
  • Where Vf is the final velocity
  • Vi is the initial velocity
  • a is the constant signed acceleration
  • t is elapsed time (zero or greater)

Multiply constant acceleration by elapsed time, then add initial velocity. The displacement route instead uses v² = u² + 2as, checks both signed velocity branches for nonnegative times, and reports the earliest arrival plus any later arrival after reversal. Use signed displacement, not total distance travelled.

Typical units for these values are m/s for velocity, m/s2 for acceleration, and seconds for time. With that said, other values can be used as long as they match up. For example, m/s could be ft/s as long as acceleration is then ft/s^2.

Final Velocity Definition

Final velocity describes both speed and direction at the endpoint. In this one-dimensional calculator its sign represents direction relative to your chosen positive axis.

Final Velocity Example

How to calculate final velocity?

First, determine the initial velocity. For this example problem, the initial velocity is measured to be 50 m/s.

Next, determine the acceleration. During the duration of the movement, this object accelerates at a rate of 5 m/s^2.

Next, determine the total time of acceleration. The object in this example accelerated for a total time of 5 seconds.

Finally, calculate the final velocity using the formula above:

Vf = Vi + a * t

Vf = 50 + 5 * 5

Vf = 75 m/s.

FAQ

What is a final velocity?

Final velocity is the signed endpoint velocity along a chosen axis; its magnitude is speed.

How is final velocity calculated?

With constant acceleration, final velocity equals initial velocity plus acceleration times elapsed time.

How to calculate final velocity?

  1. First, determine the initial velocity.

    Measure the initial velocity.

  2. Next, determine the acceleration.

    Determine the constant signed acceleration.

  3. Next, determine the time.

    Measure the total time.

  4. Finally, calculate the final velocity.

    Calculate the final velocity using the formula above.