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Appendix - 60 Appendix A Graphing a Linear Function...

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60 Appendix A Graphing a Linear Function Consider an object that is moving at constant velocity v o , until at a certain time it is given a constant acceleration a in the direction of motion. In this case the velocity v at a later time is given by v = v o + at where t is the time measured from the time of application of a. (See Chapter 1 of your text). Knowing this fact, suppose you wanted to investigate experimentally to see if a certain object moving in a straight line was undergoing constant acceleration. Suppose, further, that to investigate this you made the following measurements of velocity at various times t. V (m/s) t (sec) 7.5 9.8 12.8 16.3 18.8 22.1 24.5 28.2 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Suppose, also, that from studying your experimental arrangement you know that the time has been measured very accurately, but the measured velocities are uncertain to ± 0.5 cm/s. How would you decide whether, within experimental error, your measurements indicate a constant acceleration? Probably the best way would be by plotting a graph of v versus t. While many people use computers now to make and analyze such plots, they do so only after they know how to make and interpret such plots manually. The purpose of this appendix is to review your knowledge of how to plot linear functions such as v = v o + at. You may have studied linear functions is the standard form y = mx + b. For example, you may have plotted y = 5x + 6 and you may have determined that such a function yields a straight line or linear plot with slope m = 5, y intercept b = 6 and x intercept -b/m = -6/5. In any case, plot y = 5x + 6 for 5 1 - x on linear (ordinary) graph paper and determine from your graph the
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61 slope and x and y intercepts. Remember that the slope is determined by using a section of
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