Speed and velocity

A car at 90 km/h covers 25 metres every second, about the length of two buses.

How fast? Speed is distance per time

Speed answers the question "how fast?". Average speed is the distance travelled divided by the time it took. A sprinter who covers 100 m in 12.5 s has an average speed of 100 ÷ 12.5 = 8 m/s. That does not mean the runner moved at exactly 8 m/s the whole time. They started from rest, sped up, and probably slowed slightly at the end. The average smooths all of that into one number.

The speed shown on a car’s speedometer is different: it is the instantaneous speed, the speed at one moment. If you could measure the distance covered in a very short time, say a hundredth of a second, and divide, you would get the instantaneous speed. Police speed guns and phone GPS apps do a version of this.

Velocity adds a direction

Velocity is speed with a direction. Average velocity is displacement divided by time: v = Δx ÷ Δt. Because it uses displacement, a round trip has an average velocity of zero even if the average speed was high. A cyclist who rides 6 km out and 6 km back in one hour has an average speed of 12 km/h and an average velocity of 0 km/h. When motion is along a straight line in one direction, average speed and the magnitude of average velocity are the same. They can differ when the path curves or turns back. Instantaneous speed is always the magnitude of instantaneous velocity.

A car going round a roundabout at a steady 30 km/h has a constant speed, but its velocity keeps changing because its direction keeps changing. This matters later: the rate of change of velocity with time is called acceleration, so a car turning at constant speed is still accelerating.

Units: metres per second and kilometres per hour

Physics uses metres per second (m/s). Road signs use kilometres per hour (km/h) or miles per hour. To convert, remember that 1 km = 1,000 m and 1 h = 3,600 s, so 1 m/s = 3,600 m per hour = 3.6 km/h. Multiply m/s by 3.6 to get km/h, and divide km/h by 3.6 to get m/s. A car at 90 km/h moves 90 ÷ 3.6 = 25 m/s. Sound in air at 20 °C travels about 343 m/s, which is roughly 1,235 km/h.

Real trips mix fast and slow stretches, so the average can hide a lot. Suppose you drive 30 km at 60 km/h and then 30 km at 30 km/h. The first part takes half an hour and the second a full hour, so 60 km takes 1.5 hours and the average speed is 40 km/h, not the 45 km/h you might guess by averaging the two speeds. The slow part lasts longer, so it counts for more. Always divide the total distance by the total time.

Using v = d ÷ t three ways

The same relation answers three kinds of question. Speed: v = d ÷ t. Distance: d = v × t, so a train at 50 m/s covers 50 × 60 = 3,000 m in a minute. Time: t = d ÷ v, so walking 1,500 m at 1.25 m/s takes 1,200 s, or 20 minutes. Always check that the units match before you divide or multiply: kilometres with hours, metres with seconds.