Speed — AQA GCSE Physics

Real journeys are not steady. A walker slows at a kerb and speeds up again, and a car accelerates away from lights, brakes for a junction and waits in traffic, so a graph of its motion is a curve rather than a straight line. This is why average speed is the quantity normally quoted: it summarises a varying journey in one number, found by dividing the whole distance by the whole time, and it says nothing about the speed at any particular moment. A car averaging 12 m/s across a town journey may have touched 20 m/s and also stood completely still. When a question asks you to calculate the average speed it is inviting the totals; when it says at this instant it wants a tangent or a single reading.

The specification names four factors and expects a reason for each. Age: the very young and the old generally move more slowly, as muscle power and stride length change. Terrain: walking uphill, on sand or over rough ground is slower than on a level pavement, because more work is done against gravity and against friction. Fitness: a trained person sustains a higher speed for longer before fatigue forces them to slow down. Distance travelled: speeds are highest over short distances and fall for longer ones, which is why a sprinter's pace could never be held for a marathon. Examiners also accept wind, the load carried, temperature and the surface underfoot. Questions ask you to suggest a factor and explain its effect, so always give both.

These three figures have to be remembered, because questions use them without supplying them: a walker about 1.5 m/s, a runner about 3 m/s and a cyclist about 6 m/s. Learn them as a doubling sequence. Check them against experience, since 1.5 m/s is roughly 5.4 km/h, which is a brisk walk, and a cyclist at 6 m/s covers a kilometre in under three minutes. The word typical matters, because an answer within a sensible range is accepted and a sprinter or racing cyclist is faster. Use the values for estimates: a 300 m walk to the shop takes about 200 s, and a runner covering 1.2 km takes around 400 s. The same style of question also asks for transport speeds, so learn a car at roughly 25 m/s as well.

Examiners expect students to recall typical speeds for human movement and transport. For a person, typical values are walking at ~1.5 m/s, running at ~3 m/s, and cycling at ~6 m/s. For transport, sensible estimates include a car on a main road at ~13-30 m/s, a train at ~50 m/s, and a passenger aircraft at ~250 m/s. These figures are crucial for estimation questions and checking calculations. If a calculated speed for a walking person is 60 m/s, a unit conversion error or misplaced decimal point is likely. Remember to convert kilometres per hour to metres per second by dividing by 3.6.

The speed of sound is a property of the material the wave travels through rather than of the source, and it changes when the material changes: about 330 m/s in air, roughly 1500 m/s in water and around 5000 m/s in steel, because particles that are closer together pass the vibration on faster. Warmer air also carries sound a little faster, so the figure for air is only a typical one. Wind speed varies constantly with the weather, with height above the ground and with the shelter of buildings and hills, which is why wind turbines are mounted on tall towers in exposed places. In both cases a single quoted number is an average or a typical figure and not a fixed constant of nature.

This is the value to use whenever a question about sound in air supplies none, and it powers two classic calculations. For an echo, the sound travels to the wall and back, so the distance in the equation is twice the separation: an echo returning after 0.40 s means the sound covered 132 m, so the wall stands 66 m away. For thunder, light arrives effectively instantly, so the delay between the flash and the bang is the sound's travel time, and a gap of 6.0 s means the strike was about 2000 m away. Sound is roughly a million times slower than light, which is why the two are treated so differently. Keep the time in seconds and the answer comes out in metres.

Measuring a speed means measuring a length and a time and then dividing one by the other. Choose the instrument to suit the size: a metre rule for a bench, a tape measure or a trundle wheel for a corridor or a track. Time with a stopwatch for anything lasting several seconds and with light gates for anything faster, because a human reaction time of around 0.2 s is a large fraction of a short interval and is the main source of random error. Repeat each timing at least three times, take a mean, and discard any obvious anomaly. Then divide the distance in metres by the time in seconds to get a speed in metres per second. Measuring over a longer distance reduces the percentage uncertainty in the timing.

This equation gives the distance covered when the speed is steady, with distance in metres, speed in metres per second and time in seconds. Rearranged, the speed is distance divided by time and the time is distance divided by speed, and any correct rearrangement is credited. Where the motion is not steady, apply the equation stage by stage and add the distances: a car at 7.5 m/s for 3.0 s covers 22.5 m, then at 15 m/s for 2.0 s covers a further 30 m, giving 52.5 m in total. The average speed for the whole journey is then the total distance divided by the total time, which here is 10.5 m/s and is not the average of the two speeds. Convert minutes and hours into seconds before substituting.