Motion in a straight line

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 of 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.

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

Method of travelTypical speed (m/s)
Walking1.5
Running 3
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. A light breeze moves at perhaps 3 m/s, but a gale would be more than 20 m/s.

Calculations involving space, distance and time

The speed of an object can be calculated using the equation:

 (average) \ speed = \frac{distance \ travelled}{time \ taken}

 v = \frac{x}{t}

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

distance travelled = average speed × time taken

 x = v \ t

This is when:

  • distance travelled (x) is measured in metres (m)
  • speed (v) is measured in metres per second (m/s)
  • time taken (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 (x):

500 + 1,500 = 2,000 m

Then calculate total time taken (t):

50 + 75 = 125 s

Then find (v):

v = \frac{x}{t}

v = 2000 ÷ 125

v = 16 m/s

Measuring speeds in the lab

To calculate the speed of an object two measurements are needed:

  • how far it travels
  • the time it takes to move that distance

These measurements can be made using different types of equipment:

EquipmentDistance measurementTime measurement
Ruler and stopwatchRuler measures distance travelled Stopwatch measures time taken
Light gates Size of object, measured with a rulerLight gate connects to a timer, which gives the reading
Video analysis Distance moved from frame to frame observed on a ruler in the picturesThe time between frames is known