5.6.1b Speed and typical values
Speed as a scalar quantity
Definition
Speed
Speed is the distance travelled per unit time, measured in metres per second (m/s\text{m/s}m/s).
- Speed is a scalar quantity: it has magnitude but no direction. A speed of 10 m/s10\ \text{m/s}10 m/s tells you how fast an object moves, but not which way.
- The speed of a moving object is rarely constant: a person speeds up or slows down, and a car’s speed changes as it accelerates, brakes, turns or stops in traffic.
Typical values of speed
- The speed a person can walk, run or cycle depends on factors including age, fitness, terrain and distance travelled.
- Typical personal speeds: walking 1.5 m/s1.5\ \text{m/s}1.5 m/s, running 3 m/s3\ \text{m/s}3 m/s and cycling 6 m/s6\ \text{m/s}6 m/s.
- Typical transport speeds: a car ≈25 m/s\approx 25\ \text{m/s}≈25 m/s, a train ≈55 m/s\approx 55\ \text{m/s}≈55 m/s and a passenger aircraft ≈250 m/s\approx 250\ \text{m/s}≈250 m/s.
- These are only typical values; actual speeds vary with the vehicle, journey and conditions.
- A typical value for the speed of sound in air is 330 m/s330\ \text{m/s}330 m/s, and wind speed also varies over time and place.
Measuring and calculating speed
- To find speed, measure the distance travelled (with a ruler or tape measure) and the time taken (with a stopwatch).
- Then v=stv = \dfrac{s}{t}v=ts.
- vvv is the speed in metres per second (m/s\text{m/s}m/s).
- sss is the distance in metres (m\text{m}m).
- ttt is the time in seconds (s\text{s}s).
- For an object moving at constant speed, rearrange to s=vts = vts=vt: distance travelled = speed × time.
Example
A cyclist travels 180 m180\ \text{m}180 m in 30 s30\ \text{s}30 s. Calculate the cyclist’s speed.
- Write the equation: v=stv = \dfrac{s}{t}v=ts.
- Substitute the values: v=180 m30 sv = \dfrac{180\ \text{m}}{30\ \text{s}}v=30 s180 m.
- Calculate the speed: v=6 m/sv = 6\ \text{m/s}v=6 m/s.
Average speed for non-uniform motion
Definition
Average speed
Average speed is the total distance travelled divided by the total time taken.
- When an object’s speed changes during a journey, use average speed=total distancetotal time\text{average speed} = \dfrac{\text{total distance}}{\text{total time}}average speed=total timetotal distance.
- The total time includes the whole journey, including any time the object is stationary.
Example
A car travels 600 m600\ \text{m}600 m in 30 s30\ \text{s}30 s and then 400 m400\ \text{m}400 m in 40 s40\ \text{s}40 s. Calculate its average speed for the whole journey.
- Write the equation: average speed=total distancetotal time\text{average speed} = \dfrac{\text{total distance}}{\text{total time}}average speed=total timetotal distance.
- Find the total distance: 600 m+400 m=1000 m600\ \text{m} + 400\ \text{m} = 1000\ \text{m}600 m+400 m=1000 m.
- Find the total time: 30 s+40 s=70 s30\ \text{s} + 40\ \text{s} = 70\ \text{s}30 s+40 s=70 s.
- Substitute the values: average speed=1000 m70 s\text{average speed} = \dfrac{1000\ \text{m}}{70\ \text{s}}average speed=70 s1000 m.
- Calculate the average speed: average speed=14.3 m/s\text{average speed} = 14.3\ \text{m/s}average speed=14.3 m/s.
Exam technique
- Do not include a direction with speed; speed is a scalar.
- For a journey with changing speed, do not average the speeds; use total distance ÷ total time.
- Check the distance is in metres and the time in seconds before giving an answer in m/s\text{m/s}m/s.
- State the equation before substituting, and for average speed find the total distance and total time first.
- Remember that values such as 1.5 m/s1.5\ \text{m/s}1.5 m/s for walking and 330 m/s330\ \text{m/s}330 m/s for sound in air are approximate typical values.
Self review
- Why is speed a scalar quantity?
- State the typical speeds for walking, running and cycling.
- What is a typical value for the speed of sound in air?
- State the equation for distance at constant speed.
- How do you calculate average speed for non-uniform motion?
