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Unformatted text preview: Recall the displacement of a particle during some time interval. As the particle moves from some initial position to some final position then the displacement is given by: i f x x x = Notice if x i > x f then the displacement is negative , whereas the distance is always positive. Distance is the length of a path followed by a particle. d x x i f = The average velocity can be defined from the displacement. t x v average = Graphs of Motion with Constant Velocity The slope of the graph is defined below. x is called the independent variable , and is plotted along the xaxis. The other variable y is called the dependent variable . If the data is plotted on a graph and a straight line can be found, then the mathematical relationship between the variables x and y is known. The x and y variables are proportional to each other, hence form the equation for a straight line: y = mx + b Positive and Negative Velocity Graphs can give you information about the motion of the object. In particular, the slope of the line on a position versus time graph gives you a measurement of velocity . This velocity is actually an average velocity. What would it mean if many of the points were not right on or very close to the best fit line? What does it mean to have a negative velocity? In order to have a negative velocity, you need a coordinate system. A negative velocity refers to a direction with respect to a defined coordinate system. It says that you are moving in a direction of decreasing values of position. In mathematics and its applications, a coordinate system is a system for assigning an ntuple of numbers or scalars to each point in an n dimensional space. A positive velocity tells us that an object is moving in a direction towards increasing values of position . It still doesnt matter where we put the zero on our coordinate system. The slope of the line gives the velocity, and the slope does not depend upon the location of zero. Remember, the negative sign refers to direction only. It does not tell us anything about the size (magnitude) of the velocity. The size (magnitude) is called speed . When speed is combined with direction, it is called velocity. Graphs If an object has constant positive velocity, the graph of position versus time will be a straight line where the slope is the velocity. The higher the velocity is, the steeper the line on the graph is since average velocity is defined to be v = x/t. The place the line begins depends on x . It can be positive, negative, or 0. If the object has negative velocity, the slope will be negative. This equation for a straight line is given be x = mt + b. Where the slope m is the velocity ( v ) of the object and the y intercept represented the initial position of the object, which we designate as x ....
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 Summer '10
 Ernest
 Physics

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