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Motion (kinematics)

Speed, distance and time

Average speed is distance travelled divided by the time it took.

v=dt
Distanced=vt
Timet=dv

Calculator

The live calculator needs JavaScript. The worked example below shows the same steps it would.

See it move

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  • At a steady 10 m/s, after 10 s you have gone 100 m. Speed is the slope of this line.

What the symbols mean

v
the average speed (m/s in the calculator) (m/s)
d
the distance travelled (m) (m)
t
the time taken (s) (s)

When to use it

Use it for journeys, races and any motion where you want an average: it does not care whether the speed changed on the way. Keep the units consistent: metres with seconds gives m/s, kilometres with hours gives km/h. To convert m/s to km/h, multiply by 3.6.

Worked example

Usain Bolt ran 100 m in 9.58 s. What was his average speed?

  1. Start from the formula.

    v=dt

  2. Substitute d = 100, t = 9.58 and work it out.

    v=1009.58
    ≈10.4384m/s

  3. In km/h, multiply m/s by 3.6 (3600 s in an hour, 1000 m in a km):

    v=10.4384·3.6
    ≈37.5783km/h

Answer v ≈ 10.44 m/s, about 37.58 km/h

Why it works

Speed is the rate of covering distance. At a steady speed the distance–time graph is a straight line and the speed is its slope.

Common mistakes

  • Mixing units, such as kilometres with seconds, without converting.
  • Averaging two speeds for an average speed: driving 60 km/h one way and 40 km/h back averages 48 km/h, not 50, because more time is spent at the slower speed.
  • Confusing speed with velocity, which also has a direction.