Motion in a straight line

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 travel Typical 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. The speed of a gentle breeze is about 4 m/s. The speed of a gale can be between 20 m/s and 30 m/s.

Calculations involving speed, distance and time

The distance travelled by an object moving at constant speed can be calculated using the equation:

distance\: travelled = speed \times time

s = v\: t

This is when:

  • distance travelled (s) is measured in metres (m) or kilometres (km)
  • speed (v) is measured in metres per second (m/s) or kilometres per hour (km/h)
  • time (t) is measured in seconds (s) or hours (h)

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 (s):

500 + 1,500 = 2,000 m

Then calculate total time taken (t):

50 + 75 = 125 s

Then rearrange s = v t to find (v):

v = \frac{s}{t}

v = 2000 \div125

\underline{v = 16\:m/s}

A train travels 50 km in 15 min, and then 30 km in a further 15 min. Calculate its average speed for the whole journey in km/h.

First calculate total distance travelled (s):

50 + 30 = 80 km

Then calculate total time taken in hours, (t):

15 min + 15 min = 30 min = 0.5 h

Then rearrange s = v t to find (v):

v = \frac{s}{t}

v = 80 \div 0.5

\underline{v=160\:km/h}