Time, Distance and Speed

In short: Speed is how much distance something covers each second: speed = distance ÷ time, or $v=\frac{d}{t}$. It is measured in metres per second (m/s) or kilometres per hour (km/h), and you divide km/h by 3.6 to get m/s.

Three things that describe motion

• Distance is how far something travels. Unit: metre (m). We also use km and cm.
• Time is how long the motion takes. Unit: second (s). We also use minutes and hours.
• Speed is how much distance is covered every second (or every hour). Unit: metres per second (m/s) or kilometres per hour (km/h).

The speed formula

$$\text{speed}=\frac{\text{distance}}{\text{time}}v=\frac{d}{t}$$

Physicists use $v$ for speed (from "velocity"), $d$ for distance and $t$ for time.

You can rearrange it in two other ways:

$$d=v\times tt=\frac{d}{v}$$

Changing units

Always check units before you put numbers into a formula.

• 1 km = 1000 m
• 1 hour = 60 minutes = 3600 s
• To change km/h to m/s, divide by 3.6
• To change m/s to km/h, multiply by 3.6

Why 3.6? Because $1\text{ km/h}=\frac{1000\text{ m}}{3600\text{ s}}=\frac{1}{3.6}\text{ m/s}$.

Average speed and instantaneous speed

Leo does not ride at exactly 5 m/s the whole way. He slows at corners and speeds up on hills. So 5 m/s is his average speed.

$$\text{average speed}=\frac{\text{total distance}}{\text{total time}}$$

Instantaneous speed is the speed at one exact moment. A car's speedometer shows instantaneous speed. A speed camera that checks your time between two points measures average speed.

Measuring speed in the lab

• Stopwatch and tape measure: simple, but your reaction time adds error (about 0.2 s).
• Light gates: a beam is broken when the object passes. A computer records time very precisely.
• Ticker timer: puts dots on a paper tape at equal time gaps. Dots far apart mean fast. Dots close together mean slow.

Quick summary

• Speed tells you how much distance is covered per unit of time.
• $v=\frac{d}{t}$, $d=vt$, $t=\frac{d}{v}$.
• Change units first: km to m, minutes or hours to seconds.
• km/h $÷$ 3.6 = m/s. m/s $\times$ 3.6 = km/h.
• Average speed = total distance ÷ total time. Never just average the speeds.
• Instantaneous speed is the speed at one moment, like a speedometer reading.

Quiz