In fact, an important way to discover physical relationships is to measure various physical quantities and then make graphs of one quantity against another to see if they are correlated in any way. It is not accidental that the same equations are obtained by graphical analysis as by algebraic techniques. Notice that this equation was also derived algebraically from other motion equations in Chapter 2.5 Motion Equations for Constant Acceleration in One Dimension. Furthermore, the slope of the graph of velocity versus time is acceleration, which is shown in Figure 3(c).Ī general relationship for velocity, acceleration, and time has again been obtained from a graph. If this is done at every point on the curve and the values are plotted against time, then the graph of velocity versus time shown in Figure 3(b) is obtained. Tangent lines are shown for two points in Figure 3(a). It is found by drawing a straight line tangent to the curve at the point of interest and taking the slope of this straight line. The slope at any point on a displacement-versus-time graph is the instantaneous velocity at that point. The slope of the curve becomes steeper as time progresses, showing that the velocity is increasing over time. The graph of displacement versus time in Figure 3(a) is a curve rather than a straight line.

(c) Acceleration has the constant value of 5.0 m/s 2 over the time interval plotted. t graph is constant for this part of the motion, indicating constant acceleration. Instantaneous velocity at any point is the slope of the tangent at that point. This is shown at two points, and the instantaneous velocities obtained are plotted in the next graph. Graphs of motion of a jet-powered car during the time span when its acceleration is constant. Time starts at zero for this motion (as if measured with a stopwatch), and the displacement and velocity are initially 200 m and 15 m/s, respectively. The graphs in Figure 3 below represent the motion of the jet-powered car as it accelerates toward its top speed, but only during the time when its acceleration is constant. Graphs of Motion when α is constant but α≠0 This is an impressively large land speed (900 km/h, or about 560 mi/h): much greater than the typical highway speed limit of 60 mi/h (27 m/s or 96 km/h), but considerably shy of the record of 343 m/s (1234 km/h or 766 mi/h) set in 1997. Using the relationship between dependent and independent variables, we see that the slope in the graph above is average velocity and the intercept is displacement at time zero-that is, Substituting these symbols into gives 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 is just such a straight-line graph. A graph of displacement versus time would, thus, have on the vertical axis and 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 is used for the y-intercept, which is the point at which the line crosses the vertical axis. Here 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 and the vertical axis the, 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. Slopes and General Relationshipsįirst note that graphs in this text have perpendicular axes, one horizontal and the other vertical. This section uses graphs of displacement, velocity, and acceleration versus time to illustrate one-dimensional kinematics. Graphs not only contain numerical information they also reveal relationships between physical quantities. time.Ī graph, like a picture, is worth a thousand words. Determine average or instantaneous acceleration from a graph of velocity vs.Determine average velocity or instantaneous velocity from a graph of position vs.Describe a straight-line graph in terms of its slope and y-intercept.

Graphical analysis of motion physics