Define speed as distance divided by time, calculate speed, distance or time, and read simple distance-time information

What this dot point is asking

This dot point wants you to know what speed means, how to work it out from distance and time, and how to rearrange the formula to find distance or time instead. You should also be able to read simple distance and time information. The big idea is that speed tells you how fast something is moving, and it is just the distance travelled divided by the time taken.

The answer

What speed means

Speed tells you how fast something is moving. It is how much distance is covered in a certain time. A fast object covers a lot of distance in a short time; a slow object covers little distance in the same time.

The most common unit for speed is metres per second (m/s). You may also see kilometres per hour (km/h), used for cars and buses.

The speed formula

Speed is worked out with this formula:

So if a runner covers 100 metres in 20 seconds, the speed is $100 \div 20 = 5\ \text{m/s}$. Make sure the distance is in metres and the time is in seconds to get an answer in m/s.

Rearranging the formula

The same formula can be turned around to find distance or time:

• To find distance: $\text{distance} = \text{speed} \times \text{time}$.
• To find time: $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.

A simple way to remember all three is the formula triangle, with distance on top, and speed and time underneath. Cover the one you want, and the triangle shows you what to do with the other two.

Steady speed and changing speed

If something moves at a steady speed (also called constant speed), it covers the same distance every second. Its speed does not change. Most exam questions at this level use a steady speed.

If the speed changes, the object is speeding up or slowing down. Speeding up is called accelerating; slowing down is called decelerating.

Average speed

Real journeys are not always at a steady speed; you might speed up, slow down and stop. The average speed is the total distance divided by the total time for the whole journey. It smooths out all the changes into one number.

Reading distance and time

A simple distance-time graph shows distance going up the side and time going across the bottom. A straight line going up means a steady speed; a steeper line means a faster speed; a flat (horizontal) line means the object is stopped, because the distance is not changing.

Examples in context

Example 1. Timing a runner on a track. At sports day, a teacher measures that a student runs the 100 metre track in 25 seconds. Using speed = distance $\div$ time, the student's speed is $100 \div 25 = 4\ \text{m/s}$. The same method is used to compare runners: whoever has the higher speed wins.

Example 2. A speed limit sign. A road sign showing 50 km/h is telling drivers the top speed allowed. Speed cameras measure how far a car travels in a known short time, then use speed = distance $\div$ time to check whether the driver is over the limit. The everyday idea of speed is exactly the science formula.

Try this

• Cue. A car travels $200\ \text{m}$ in $10\ \text{s}$. Work out its speed. Speed = distance $\div$ time = $200 \div 10 = 20\ \text{m/s}$.

• Cue. A walker moves at $2\ \text{m/s}$ for $30\ \text{s}$. How far do they walk? Distance = speed $\times$ time = $2 \times 30 = 60\ \text{m}$.

• Cue. On a distance-time graph, describe what a flat horizontal line shows. A flat line shows the object is not moving (it is stopped), because the distance is not changing as time goes on.