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Difference Between Velocity and Speed

In common usage, people use "velocity" and "speed" interchangeably as if they were the same. But they're actually different. Velocity includes two properties: a magnitude and a direction. Speed is just the magnitude of the velocity. If one car is traveling east on a highway at 60 mph and another one is traveling west on the same highway at 60 mph, they have different velocities because their directions are different, but they have the same speed.

If you're standing on the side of the highway and the first car goes by, it would seem to be going pretty fast. But if you're in one of the cars when the other passes, it seems to be going twice as fast since the difference between the velocities including their directions is 120 mph. (By including their directions, the first car has a velocity of +60 mph in the eastern direction while the second car has a velocity of -60 mph in the eastern direction; the difference is 60 - -60 = 120 mph.)

Another way to illustrate the importance of direction in velocity is to think about what happens in the following two very different situations:

  1. Situation 1: one car is traveling 62 mph east and bumps into the back of a second car going 60 mph in the same direction. That's annoying, but nobody gets hurt and the damage to the cars is probably not too bad.
  2. Situation 2: one car traveling 62 mph west in the eastbound lane crashes head on into a second car going 60 mph east. Unfortunately, this is a very serious accident in which one or more people probably die.

Note that the speed of the first car was the same in the two situations, but it's direction and therefore its velocity were very different. Unfortunately, so were the outcomes.

The distinction between velocity and speed is also important when comparing straight-line and circular motion. If an object travels 10 meters/second in a straight line for 1 hour, the distance (or displacement) between its starting and final positions is 60*60*10 or 36,000 meters. But if the tip of a 50 meter wind turbine blade rotates around the wind turbine's nacelle with the same speed of 10 meters/second, after 1 hour, it's at most 100 meters from its starting location. Again, we have the same speed in both cases, but different velocities, and the outcome is very different.

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