Physics I For Dummies
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In physics, velocity, which is the rate of change of position (or speed in a particular direction), is a vector. Imagine that you just hit a ground ball on the baseball diamond and you’re running along the first-base line, or the s vector, 90 feet at a 45-degree angle to the positive x-axis. But as you run, it occurs to you to ask, “Will my velocity enable me to evade the first baseman?” A good question, because the ball is on its way from the shortstop.

Whipping out your calculator, you figure that you need 3.0 seconds to reach first base from home plate; so what’s your velocity? To find your velocity, you quickly divide the s vector by the time it takes to reach first base:


This expression represents a displacement vector divided by a time, and time is just a scalar. The result must be a vector, too. And it is: velocity, or v:


Your velocity is 30 feet/second at 45 degrees, and it’s a vector, v.

Dividing a vector by a scalar gives you a vector with potentially different units and the same direction.

In this case, you see that dividing a displacement vector, s, by a time gives you a velocity vector, v. It has the same magnitude as when you divided a distance by a time, but now you see a direction associated with it as well, because the displacement, s, is a vector.

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Dr. Steven Holzner has written more than 40 books about physics and programming. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Dr. Holzner received his PhD at Cornell.

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