Speed: the distance covered every second
Definition
Speed
The distance travelled per unit time.
v=st v = \frac{s}{t} v=tswhere vvv is the speed in m/s\text{m/s}m/s, sss is the distance in m\text{m}m and ttt is the time in s\text{s}s.
- A speed of 8 m/s8\ \text{m/s}8 m/s means 8 m8\ \text{m}8 m is covered in every second; "how fast it goes" describes speed but does not define it.
- Rearrange the same equation as the question needs: s=v×ts = v \times ts=v×t for a distance, t=s/vt = s/vt=s/v for a time.
- The SI unit is m/s\text{m/s}m/s, but km/h\text{km/h}km/h and cm/s\text{cm/s}cm/s are also used.
- Keep the units consistent: whatever units go in set the unit that comes out, so a distance in km\text{km}km with a time in h\text{h}h gives a speed in km/h\text{km/h}km/h.
- Convert with 1 km=1000 m1\ \text{km} = 1000\ \text{m}1 km=1000 m and 1 h=3600 s1\ \text{h} = 3600\ \text{s}1 h=3600 s, which together give 1 m/s=3.6 km/h1\ \text{m/s} = 3.6\ \text{km/h}1 m/s=3.6 km/h.
Velocity: speed with a direction attached
Definition
Velocity
Speed in a given direction.
- A velocity is only fully stated with a direction: 8.0 m/s8.0\ \text{m/s}8.0 m/s due north, or 12 m/s12\ \text{m/s}12 m/s downwards; a speed needs only a number and a unit.
- The same equation v=s/tv = s/tv=s/t gives the velocity when an object moves in a straight line in one fixed direction.
- An object can travel at constant speed while its velocity changes, because a change of direction alone changes the velocity.
- A car going round a roundabout at a steady 8.0 m/s8.0\ \text{m/s}8.0 m/s keeps its speed but has a continuously changing velocity, since the direction it heads in changes every instant.
Average speed: total distance over total time
Definition
Average speed
average speed=total distance travelledtotal time taken
\text{average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}
average speed=total time takentotal distance travelled
- Real journeys are not steady: a bus speeds up, slows down and stops.
- A single value of v=s/tv = s/tv=s/t across the whole trip is only the average speed, the steady speed that would cover the same distance in the same time.
- That is different from the instantaneous speed, the speed at one moment, which is what a speedometer shows.
- The marks live in the word total: the total time includes every part of the journey, including any time spent stationary at lights or in a queue.
Common Mistake
- Constant speed does not mean constant velocity. An object turning a corner keeps its speed but changes its velocity, because its direction changes.
- Do not average the speeds. Adding two speeds and halving only works if the two stages take exactly the same time; always go back to total distance over total time.
- Do not drop stationary time from the total time; a stop still lasts, and it drags the average speed down.
- Do not mix units inside one substitution: convert km\text{km}km to m\text{m}m and hours or minutes to seconds before substituting if the answer is wanted in m/s\text{m/s}m/s.
Exam technique
- Write the equation from recall before substituting; marks are staged, so a correct equation and substitution still score even if the arithmetic slips, and the final answer needs its unit.
- Match the command word: "define speed" needs the wording distance travelled per unit time; "state the velocity" needs a number, a unit and a direction.
- The word average signals that the motion was not steady, so use total distance over total time, not one stage.
- If the data is in km\text{km}km and h\text{h}h but the answer is wanted in m/s\text{m/s}m/s, convert first and show the conversion.
Self review
- Define speed, and give the equation with its unit.
- What extra information does a velocity carry that a speed does not?
- How can an object have a constant speed but a changing velocity?
- How do you find the average speed for a journey that includes a stop?
- Convert 20 m/s20\ \text{m/s}20 m/s into km/h\text{km/h}km/h.