alt="Schematic illustration of examining displacement with a golf ball."/>
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.
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:
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
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 in the x position,
The change in the y location is
If you’re more interested in figuring out the magnitude (size) of the displacement than in the changes in the x and y locations of the golf ball, that’s a different story. The question now becomes: How far is the golf ball from its starting point at the center of the graph?
So in this case, the magnitude of the ball’s displacement is exactly 5 meters.
Determining direction
Therefore, the angle itself is just the inverse tangent of that:
The ball (refer to Figure 3-2) has moved at an angle of 37° from the x-axis.
Speed Specifics: What Is Speed, Anyway?
There’s more to the story of motion than just the actual movement. When displacement takes place, it happens in a certain amount of time. You may already know that speed is distance traveled per a certain amount of time:
