Speed and velocity are not the same thing
The Sunday Nation
Nairobi,
17 February 2013
Robert Dreezy asks a question that sound as if it should be in a school exam: “What is the difference between speed and velocity?” Well; both have something to do with the pace of motion, that is, how much distance is covered in a given amount of time. In normal, everyday conversation (and writing), the two terms are used interchangeably, but they are quite different.
The difference is that velocity is concerned with distance in a particular direction while speed is just distance along the path taken. When David Rudisha broke the 800m world record at the London Olympics, he clocked one minute, 40.91 seconds. This works to an average speed of 7.93 metres per second (800m divided by 100.91s), which is equivalent to 28.54 kilometres per hour.
That’s the speed; the average velocity is evaluated in a different way. We only need to know three things: the starting point, the end and the time taken. Now athletes in the 800m race do not start in a straight line across the track; they are staggered. The runner in lane 2 starts 3.526m ahead of lane 1; lane 3 starts 3.858m in front of lane 2 and so on. This staggering is necessary to compensate for the circular portion of the racetrack.
In the record-breaking race, Rudisha started off in lane 4; therefore, he was a total of 11.26m ahead of the of the start/finish line. He then finished the race in lane 1, so the straight-line distance from the starting point to the end is about 11.26m… strictly speaking, it is slightly more because of the triangle formed by Rudisha, the start of lane 4 and the end of lane 1. Avoiding complicated trigonometry; we can safely call it 12m.
Thus, in that spectacular race, Rudisha only managed to move just 12m backwards! Remember, velocity has direction. So, his average velocity was only 0.12 metres per second (12m dived by 100.91s), or 0.43km/h. Now imagine a person running in lane one: he starts and finishes at the same point… average velocity is zero! “Luckily”, in the 800m final at the London Olympics, there was no athlete in lane 1 – phew!
However, we can look at different parts of the race and evaluate the corresponding velocities; especially the straight sections of the track. These are about 70m long and on the first one, Rudisha clocked about 9 seconds. That’s a velocity of about 7.8m/s (28km/h). He completed the second one in about 13s (5.4m/s or 19.4km/h).
The race can be broken in this manner into even smaller section, perhaps just a millimetre long or even shorter! This would produce numerous velocities (800,000 or more values) as Rudisha ran from start to finish.
Now imagine if the portions are made so small that they are just slightly above zero; the velocities evaluated in such a case would be for every instant of the race. In that case, we would be talking about instantaneous velocity.
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