Motion in One Dimensionb
Introduction
The purpose of this section is to introduce the concepts of displacement, velocity, and acceleration. For the sake of simplicity, we shall restrict our attention to 1-dimensional motion.
Displacement
Consider a body moving in 1 dimension: e.g., a train traveling down a straight railroad track, or a truck driving down an interstate in Kansas. Suppose that we have a team of observers who continually report the location of this body to us as time progresses. To be more exact, our observers report the distance of the body from some arbitrarily chosen reference point located on the track on which it is constrained to move. This point is known as the origin of our coordinate system. A positive value implies that the body is located meters to theright of the origin, whereas a negative value implies that the body is located meters to the left of the origin. Here, is termed the displacement of the body from the origin. See Fig. 2. Of course, if the body is extended then our observers will have to report the displacement of some conveniently chosen reference point on the body (e.g., its centre of mass) from the origin.
Our information regarding the body's motion consists of a set of data points, each specifying the displacement of the body at some time . It is usually illuminating to graph these points. Figure 3 shows an example of such a graph. As is often the case, it is possible to fit the data points appearing in this graph using a relatively simple analytic curve. Indeed, the curve associated with Fig. 3 is | (11) |
| Figure 2: Motion in 1 dimension |
| Figure 3: Graph of displacement versus time |
Velocity
Both Fig. 3 and formula (11) effectively specify the location of the body whose motion we are studying as time progresses. Let us now consider how we can use this information to determine the body's instantaneous velocity as a function of time. The conventional definition of velocity is as follows:
Velocity is the rate of
The purpose of this section is to introduce the concepts of displacement, velocity, and acceleration. For the sake of simplicity, we shall restrict our attention to 1-dimensional motion.
Displacement
Consider a body moving in 1 dimension: e.g., a train traveling down a straight railroad track, or a truck driving down an interstate in Kansas. Suppose that we have a team of observers who continually report the location of this body to us as time progresses. To be more exact, our observers report the distance of the body from some arbitrarily chosen reference point located on the track on which it is constrained to move. This point is known as the origin of our coordinate system. A positive value implies that the body is located meters to theright of the origin, whereas a negative value implies that the body is located meters to the left of the origin. Here, is termed the displacement of the body from the origin. See Fig. 2. Of course, if the body is extended then our observers will have to report the displacement of some conveniently chosen reference point on the body (e.g., its centre of mass) from the origin.
Our information regarding the body's motion consists of a set of data points, each specifying the displacement of the body at some time . It is usually illuminating to graph these points. Figure 3 shows an example of such a graph. As is often the case, it is possible to fit the data points appearing in this graph using a relatively simple analytic curve. Indeed, the curve associated with Fig. 3 is | (11) |
| Figure 2: Motion in 1 dimension |
| Figure 3: Graph of displacement versus time |
Velocity
Both Fig. 3 and formula (11) effectively specify the location of the body whose motion we are studying as time progresses. Let us now consider how we can use this information to determine the body's instantaneous velocity as a function of time. The conventional definition of velocity is as follows:
Velocity is the rate of