Distance, speed and velocity: the speed equation, rearranging it for distance and time, and recalling typical speeds for walking, running, cycling and sound.

What this dot point is asking

Edexcel statements 2.5 and 2.6 want you to recall that velocity is speed in a stated direction, to recall and use the speed equation in both its forms, and to recall typical everyday speeds for walking, running, cycling, driving and sound in air.

The speed equation

This is one of the equations you must recall from memory; it is not on the equation sheet. The same relationship rearranges three ways, so before substituting decide which quantity you are finding. To find distance, use $x = v \times t$; to find time, use $t = \dfrac{x}{v}$.

Average versus instantaneous speed

A car on a real journey speeds up, slows down and stops at lights, so its instantaneous speed is constantly changing, but its average speed is just the whole distance divided by the whole time. Many Edexcel questions deliberately use the word "average" to remind you to use total distance and total time.

Typical speeds

These rough figures let you sanity-check answers and appear in their own short-answer questions. The actual speed of a person also depends on factors such as age, terrain, fitness and the wind, which Edexcel may ask you to mention. Wind is a particularly common example: a tailwind raises a cyclist's or runner's speed while a headwind lowers it, and Edexcel sometimes asks you to compare two journeys where only the wind differs.

How Edexcel examines this

Speed questions appear on both Foundation and Higher papers, usually as a short calculation worth two or three marks, but they are also embedded in larger questions on graphs, momentum and energy, so fluency here pays off everywhere. Three habits secure the marks. First, write the equation down before substituting, because the mark scheme often awards a mark for the correct equation even if the arithmetic slips. Second, convert every quantity to SI units first: kilometres to metres (multiply by $1000$) and minutes or hours to seconds, since a single missed conversion is the most common reason answers come out a factor of $60$ or $1000$ wrong. Third, quote the unit with the answer, because a bare number rarely earns the final mark. When a question gives a journey in several stages, find the total distance and the total time separately and divide once at the end, rather than averaging the individual speeds, which does not give the correct overall average.

Try this

Q1. A car travels $750\,\text{m}$ in $30\,\text{s}$. Calculate its average speed. [2 marks]

• Cue. $v = \dfrac{x}{t} = \dfrac{750}{30} = 25\,\text{m/s}$.

Q2. State the approximate speed of sound in air. [1 mark]

• Cue. About $330\,\text{m/s}$.