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Distance
When motion is discussed, distance usually refers to how far something has travelled along a path. The symbol s is used to denote the distance an object has travelled. For example, the soccer ball in Figure 3.1 has travelled a distance of 20 metres.
Figure 3.1 Distance travelled by a soccer ball
Displacement
Unlike distance, displacement describes how far and in which direction something has travelled from an initial starting point. Displacement is the change in an object’s position from the initial point. Displacement is denoted with the symbol s . The arrow above the symbol denotes that it is a vector, meaning that it has both size and a direction. You can remember this by thinking about displacement, s, as relating to spatial location in which distance and direction matter.
Figure 3.2 If you ended up on Island B, your displacement would be 20 km east from your starting position.
Consider a person who walks six metres forwards from point A to point B, and then two metres backwards to point C. The distance that they have travelled is eight metres. However, since they have only ended up four metres from the starting position, the displacement from their starting point, A, is four metres forwards.
The total distance travelled from A to C is s = 6 + 2 = 8 m.
The displacement from A to C is s = 6 – 2 = 4 m to the right.
Figure 3.3 The walk described can be represented using arrows, where the length of the arrow symbolises the magnitude, and the direction of the arrow shows the direction of motion.
Speed
Speed is a general term for how fast something travels. It is a measure of the rate at which an object travels a distance. In other words, speed is the distance (s) travelled divided by the amount of time (t) it took to travel that distance.
Speed is used to judge how fast something is moving, or how far something will travel in a certain amount of time. Speed is commonly measured in units of metres per second (m/s), or kilometres per hour (km/h). However, depending on the motion, speed may sometimes be measured in m/min, cm/h, or even km/s.
Consider the examples of motion shown in Figure 3.4.
A rocket can travel at 11 km/s.
A cheetah maintain speed of 31 m/s.
The speed of a snail is more likely to be measured in units of cm/min.
The speed of cars is usually measured in km/h.
Speed is calculated as follows:
A simple way to remember this equation is by using the average speed triangle shown in Figure 3.5.
Using the average speed triangle, you can derive formulas for:
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