Physics I For Dummies. Steven Holzner

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

Chapter 3

      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.

You already have an intuitive feeling for what we discuss in this chapter, or you wouldn’t be able to drive or even ride a bike. Displacement is about where you are, speed is about how fast you’re going, and anyone who’s ever been in a car knows about acceleration. These characteristics of motion concern people every day, and physics has made an organized study of them. This knowledge has helped people to plan roads, build spacecraft, organize traffic patterns, fly, track the motion of planets, predict the weather, and even get mad in slow-moving traffic jams. Understanding movement is a vital part of understanding physics, and that’s the topic of this chapter. Time to move on.

Going the Distance with Displacement

      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.

The golf ball rolls over to a new point, 3 meters to the right, as you see in Figure 3-1, diagram B. The golf ball has moved, so displacement has taken place. In this case, the displacement is just 3 meters to the right. Its initial position was 0 meters, and its final position is at +3 meters. The displacement is 3 meters.

      

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 s_i, which describes initial position, (the i stands for initial). And you may see the term s_f used to describe final position.

      In these terms, moving from diagram A to diagram B in Figure 3-1, s_i is at the 0-meter mark and s_f 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 s_i to a final position s_f 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

Motion that takes place in the world isn’t always in one dimension. Motion can take place in two or three dimensions. And if you want to examine motion in two dimensions, you need two intersecting meter sticks (or number lines), called axes. You have a horizontal axis (the x-axis) and a vertical axis (the y-axis). (For three-dimensional problems, watch for a third axis (the z-axis) sticking straight up out of the paper.)

      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