Speed, distance and time

Distance is how far an object moves. It does not include an associated direction, so distance is a scalar quantity.

Speed is the rate of change of distance - it is the distance travelled per unit time. Like distance, speed also does not have an associated direction, so it is a scalar quantity.

Typical speeds

When people walk, run, or travel in a car their speed will change. They may speed up, slow down or pause for traffic. The speed at which a person can walk, run or cycle depends on many factors including:

  • age
  • terrain
  • fitness
  • distance travelled

Some typical values for speed in metres per second (m/s) include:

Method of travelTypical speed in m/s
Walking1.5
Running3
Cycling6
Car13-30
Train50
Aeroplane250

It is not only moving objects that have varying speed. The speed of the wind and the speed of sound also vary. A typical value for the speed of sound in air is about 330 m/s.

Calculations involving speed, distance and time

The average speed of a moving object can be calculated using the equation:

average~speed = \frac{distance~travelled}{time}

v = \frac{s}{t}

This is when:

  • average speed (v) is measured in metres per second (m/s)
  • distance travelled (s) is measured in metres (m)
  • time (t) is measured in seconds (s)

Example

A car travels 500 m in 50 s, then 1,500 m in 75 s. Calculate its average speed for the whole journey.

First calculate total distance travelled:

500 + 1,500 = 2,000~m

Then calculate total time taken:

50 + 75 = 125~s

Then use v = \frac{s}{t}

To find v:

v = \frac{s}{t}

v = \frac{2,000}{125}

v = 16~m/s

Converting units

It is important in motion calculations to be able to easily convert between units, in particular between metres and kilometres, and seconds and hours.

1 metre is equal to 0.001 kilometres so to convert from metres to kilometres - divide by 1,000.

1 kilometre is equal to 1,000 metres so to convert from kilometres to metres - multiply by 1,000.

1 hour is equal to 3,600 seconds so to convert from hours to seconds - multiply by 3,600.

For example:

Question

Convert the following into kilometres:

  1. 12,300 m
  2. 5,389 m
  3. 252 m
  4. 64 m

Answers

  1. 12,300 m = 12.3 km
  2. 5,389 m = 5.389 km
  3. 252 m = 0.252 km
  4. 64 m = 0.064 km
Question

Convert the following into seconds:

  1. 1.5 h
  2. 12 h
  1. 1.5 h = 5,400 s
  2. 12 h = 43,200 s
Question

Convert 1 m/s into km/h.

  1. 1 m/s = 3,600 m/h
  2. 3,600 m/h = 3.6 km/h