Section 1 of 8Speed and the basic equation
Speed is the distance travelled per unit time. It tells us how fast an object is moving:
speed = distance ÷ time, or v = s / t
Here v is the speed in metres per second (m/s), s is the distance in metres (m) and t is the time in seconds (s).
Speed is a scalar: it has size (magnitude) only. Velocity is a vector: it has both size and direction. A car travelling at 20 m/s north and another at 20 m/s east have the same speed but different velocities.
Section 2 of 8Average and instantaneous speed
Real motion is rarely at a steady speed.
- and the instantaneous speed is the gradient of the tangent at that moment (1.1.1).
A journey of 90 km that takes 1.5 h has an average speed of 60 km/h, even if the car was stationary at some moments and travelling faster than 60 km/h at others.
Section 3 of 8Units and conversions
The SI unit of speed is the metre per second, m/s. Road speeds are given in km/h. To convert:
Always make sure that the units match the equation. If the speed is in m/s, the distance must be in metres and the time in seconds. If you use km and hours, the speed comes out in km/h. Mixing km with seconds is a common source of wrong answers.
Section 4 of 8Typical speeds
It helps to know the sizes of everyday speeds, so you can check whether an answer is sensible:
| Object | Approximate speed |
|---|---|
| Walking | 1.5 m/s |
| Running | 5 m/s |
| Cycling | 6 m/s |
| Car on a motorway | 30 m/s |
| Sound in air | 330 m/s |
| Light in a vacuum | 3.0 × 10⁸ m/s |
Speed links to acceleration (1.1.4), which is the rate of change of velocity, and to the graphs in 1.1.5.
Section 5 of 8Where speed matters in practice
Speed measurement is part of everyday life.
- or 90 km/h.
- although the top speed reached will be more because the start is slower.
In an exam you may be told to use the equation as a 'formula triangle', or to rearrange it.
- and give the final answer with a unit and sensible significant figures.
- (usually two or three)
Finally, remember that when a question gives a speed in km/h and a time in minutes, the simplest approach is to convert both to the same system before you substitute, either m/s and s or km/h and h.
Section 6 of 8Worked examples
A car travels 150 km in 2.5 hours. Find its average speed in km/h and in m/s.
v = s / t = 150 ÷ 2.5 = 60 km/h.
What the symbols mean: v = speed (m s−1) · d or s = distance (m) · t = time (s)In m/s: 60 ÷ 3.6 = 16.7 m/s.
A runner moves at an average speed of 4.5 m/s. How far does she run in 8.0 minutes?
Time = 8.0 × 60 = 480 s.
s = v t = 4.5 × 480 = 2160 m (2.2 km).
Sound travels at 330 m/s. A student sees lightning and hears the thunder 6.0 s later. How far away is the lightning? (Assume the light arrives instantly.)
s = v t = 330 × 6.0 = 1980 m, about 2.0 km.
Section 7 of 8Key terms
| Term | Meaning |
|---|---|
| Speed | Distance travelled per unit time, a scalar. |
| Velocity | Speed in a stated direction, a vector. |
| Average speed | Total distance divided by total time. |
| Scalar | A quantity with size only. |
| Vector | A quantity with size and direction. |