Physics I For Dummies. Steven Holzner

Physics I For Dummies - Steven Holzner


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is very simple, but when you put them together, they’re very powerful.

      Exploring the Need for Speed

      IN THIS CHAPTER

      

Getting up to speed on displacement

      

Dissecting different kinds of speed

      

Going with acceleration

      

Examining the link among acceleration, time, and displacement

      

Connecting velocity, acceleration, and displacement

      There you are in your Formula 1 racecar, speeding toward glory. You have the speed you need, and the pylons are whipping past on either side. You’re confident that you can win, and coming into the final turn, you’re far ahead. Or at least you think you are. Seems that another racer is also making a big effort, because you see a gleam of silver in your mirror. You get a better look and realize that you need to do something — last year’s winner is gaining on you fast.

      It’s a good thing you know all about velocity and acceleration. With such knowledge, you know just what to do: You floor the gas pedal, accelerating out of trouble. Your knowledge of velocity lets you handle the final curve with ease. The checkered flag is a blur as you cross the finish line in record time. Not bad. You can thank your understanding of the issues in this chapter: displacement, velocity, and acceleration.

      When something moves from Point A to Point B, displacement takes place in physics terms. In plain English, displacement is a distance in a particular direction.

      

Like any other measurement in physics (except for certain angles), displacement always has units — usually centimeters or meters. You may also use kilometers, inches, feet, miles, or even light-years (the distance light travels in one year, a whopper of a distance not fit for measuring with a meter stick: 5,865,696,000,000 miles, which is 9,460,800,000,000 kilometers or 9,460,800,000,000,000 meters).

      In this section, we cover position and displacement in one to three dimensions.

      Understanding displacement and position

      You find displacement by finding the distance between an object’s initial position and its final position. Say, for example, that you have a fine new golf ball that’s prone to rolling around, as shown in Figure 3-1. This particular golf ball likes to roll around on top of a large measuring stick. You place the golf ball at the 0 position on the measuring stick, as you see in Figure 3-1, diagram A.

      FIGURE 3-1: Examining displacement with a golf ball.

      

In physics terms, you often see displacement referred to as the variable s (don’t ask me why).

      Scientists, being who they are, like to go into even more detail. You often see the term si, which describes initial position, (the i stands for initial). And you may see the term sf used to describe final position.

      In these terms, moving from diagram A to diagram B in Figure 3-1, si is at the 0-meter mark and sf is at +3 meters. The displacement, s, equals the final position minus the initial position:

      

Displacements don’t have to be positive; they can be zero or negative as well. If the positive direction is to the right, then a negative displacement means that the object has moved to the left.

      In diagram C, the restless golf ball has moved to a new location, which is measured as –4 meters on the measuring stick. The displacement is given by the difference between the initial and final position. If you want to know the displacement of the ball from its position in diagram B, take the initial position of the ball to be

; then the displacement is given by

      

When working on physics problems, you can choose to place the origin of your position-measuring system wherever is convenient. The measurement of the position of an object depends on where you choose to place your origin; however, displacement from an initial position si to a final position sf does not depend on the position of the origin because the displacement depends only on the difference between the positions, not the positions themselves.

      Examining axes

      Finding the distance

      Take a look at Figure 3-2, where a golf ball moves around in two dimensions. The ball starts at the center of the graph and moves up to the right. In terms of the axes, the golf ball moves to +4 meters on the x-axis and +3 meters on the y-axis, which is represented as the point (4, 3); the x measurement comes first, followed by the y measurement: (x, y).

      FIGURE 3-2: A ball moving in two dimensions.

      So what does this mean in terms of displacement? The change


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