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Velocity Calculator

With initial velocity u 5 m/s, acceleration a 2 m/s², time t 10 s, velocity comes to 25.0000 m/s — final velocity. It is reached in 5 steps, the last of which is 5 + 2 * 10, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, not an approximation fitted to it.

Final velocity from a starting velocity, a constant acceleration and a time, with the distance covered and the average velocity over the interval.

Formula and sources checked · How we check

Initial velocity u 5 m/s, Acceleration a 2 m/s², Time t 10 s

25.0000 m/s

Final velocity for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

Final velocity
25.0000 m/s
Final velocity v = u + at
5 + 2 * 1025 m/s
Average velocity
(5 + 25) / 215 m/s
Distance covered
5 * 10 + 0.5 * 2 * 10 ^ 2150 m
Final velocity in km/h
25 * 3.690 km/h
Final velocity in mph
25 / 0.4470455.923 mph

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Worked example

Starting at 5 m/s and gaining 2 m/s every second for 10 seconds finishes at 25 m/s — 90 km/h. The distance is 150 m, which is the average velocity of 15 m/s times the 10 seconds, not the final velocity times the time. Using the final figure would put the answer at 250 m and it is the commonest slip in this calculation.

How to work it out yourself

  1. 1.The acceleration has to be constant over the whole interval. A car that accelerates hard then coasts needs the two stretches worked separately.
  2. 2.Braking is a negative acceleration. Enter it as a negative number and the final velocity falls; if it goes below zero the object has reversed, which is usually not what a braking problem means.
  3. 3.The distance uses the average velocity, not the final one. Halfway between start and finish is the right speed to multiply by the time.

The formula

  1. Final velocity v = u + at5 + 2 * 10
  2. Average velocity(5 + 25) / 2
  3. Distance covered5 * 10 + 0.5 * 2 * 10 ^ 2
  4. Final velocity in km/h25 * 3.6
  5. Final velocity in mph25 / 0.44704

Source: NIST Special Publication 811 — guide for the use of the SI, BIPM — the SI Brochure, base and derived units

Questions people actually ask

What is the difference between speed and velocity?
Velocity has a direction and speed does not. In one dimension the difference shows up as the sign: −10 m/s and +10 m/s are the same speed and opposite velocities, and only the signed version gives the right answer when something reverses.
How long does it take to stop?
Set the final velocity to zero and rearrange: t = −u/a. A car at 25 m/s braking at −8 m/s² stops in 3.125 seconds, and covers 39.0625 m doing it — which is why stopping distances grow with the square of the speed.
What acceleration does gravity give?
9.80665 m/s² by the standard definition, near enough 9.81. An object dropped from rest is at 9.80665 m/s after one second and has fallen 4.903 m, ignoring air resistance — which stops being ignorable after about a second.

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