Thus a graph of displacement versus time gives a general relationship among displacement, velocity, and time, as well as giving detailed numerical information about a specific situation. Substituting these symbols into y = mx + b gives Using the relationship between dependent and independent variables, we see that the slope in the graph above is average velocity or \boldsymbol and the intercept is displacement at time zero-that is, x 0. Graph of displacement versus time for a jet-powered car on the Bonneville Salt Flats. It shows a graph of displacement versus time for a jet-powered car on a very flat dry lake bed in Nevada. Figure 2 shown below is just such a straight-line graph. A graph of displacement versus time would, thus, have x on the vertical axis and t on the horizontal axis. Time is usually an independent variable that other quantities, such as displacement, depend upon. The equation for a straight line is y = mx + b. The letter b is used for the y-intercept, which is the point at which the line crosses the vertical axis. Here m is the slope, defined to be the rise divided by the run (as seen in the figure) of the straight line. If we call the horizontal axis the x-axis and the vertical axis the y-axis, as in Figure 1 a straight-line graph has the general form When two physical quantities are plotted against one another in such a graph, the horizontal axis is usually considered to be an independent variable and the vertical axis a dependent variable. The two PHET simulations mentioned in the previous chapter are embedded here, so you can play with them now.įirst note that graphs in this text have perpendicular axes, one horizontal and the other vertical. Please note that this uses Flash so it might not run on all computers. y=bx) to see how they add to generate the polynomial curve. View the curves for the individual terms (e.g. The shape of the curve changes as the constants are adjusted. ![]() The data from a Motion Detector is a directed distance, so it can easily be used to calculate velocity.PHET EXPLORATIONS: Simulations to help you understand the concept Graphing Slope-Intercept Graphing Slope Intercept.ĭirect link: Graphing Straight Lines Graphing Straight Lines. Velocity can, therefore, be either positive or negative depending upon your direction of motion. ![]() If we consider only motion on the positive side of the origin, motion away from the origin is a positive change in position, while motion toward the origin is a negative change in position. ![]() Position is the directed distance from a chosen starting point, or origin. On the other hand, velocity is the rate of change of position. Since the distance you have traveled is always positive, speed is always positive. In other words, speed tells how fast you are traveling, but without regard to direction. So what is the difference? Speed is how far you have gone, divided by the time it took to move. Speed and velocity are often confused since the terms are sometimes used interchangeably, but they are not the same thing. In this activity, you will learn more about how these four quantities are related. When you walk, ride a bike, or travel in a car, you are often interested in the distance traveled, the time it took, and the speed or velocity of your motion.
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