Direction and speed: velocity

Introduction

Speed is a measurement that tells how quickly an object travels between two points. Velocity is a similar measurement. Unlike speed, however, velocity also measures the direction an object moves in.

Distance vs. displacement

Distance is the space between two places. It is simply measured in metres (m). Displacement, however, not only refers to the distance between two places but their relative locations as well. Say you walk 5m to the east, for example. At this point, your displacement and distance covered would both be 5m. If you were to turn around and walk 5m back west, you would have walked a distance of 10m. Your displacement, however, would be 0m because your position has not changed. If you were only to walk back 3m, your displacement would be 2m.

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Speed vs. velocity

The difference between distance and displacement is similar to the difference between speed and velocity. Speed is a measure of how quickly something is moving, but it does not consider the direction in which the movement is happening. Velocity, on the other hand, takes into consideration displacement and time taken for that displacement.

The equation for velocity is very similar to the equation for speed:

Even though the equations are very similar, they can produce very different results. Let's use the example from before. If it takes you 3 seconds (s) to walk 5m to the east, your speed and velocity are the same number: 1.67 metres per second (m/s). Your velocity would be stated as 1.67 m/s east. Then if you were to walk back 5m in 5 seconds, your speed would be (5 + 5) (3 + 5) or 1.25 m/s. Your velocity, however, would be 0 m/s because your displacement would be zero.

Displacement is not just measured back and forth, however. It can be measured in two or three dimensions. Let's say you are going on a hike. You walk 50m to the north, then you reach a fork in the path and walk 50m east. You realise you have gone the wrong way, turn around and walk 100m west. You turn and head north for 50m, then you turn and walk east for 50m. Your time for this walk was 1 minute and 40 seconds, or 100 seconds. Your speed would be (50+50+100+50+50) 100 = 3 m/s. Your velocity, on the other hand, would be 100 100 = 1 m/s north (because your displacement is 100m north of your original position).

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Velocity consists of a number and a direction. The number is called the magnitude. Like speed, a velocity's magnitude is measured in a unit of distance divided by a unit of time. Also like speed, most physicists measure the magnitude of velocity in m/s. The direction component of velocity is usually expressed in terms of compass directions, such as north, south, east and west.

Displacement-time graphs

As with speed and distance-time graphs, displacement-time graphs can be useful in representing the velocity of an object. Displacement-time graphs show displacement on the vertical (y) axis and time on the horizontal (x) axis. This example of a displacement-time graph shows an object that travels in one direction, stops, then returns.

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As with a distance-time graph, the velocity of an object can be determined by finding the slope of the line - that is, dividing the rise by the run.