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Unformatted text preview: Chapter 7 One-Dimensional Motion: The Constant Acceleration Equations 39 7 One-Dimensional Motion: The Constant Acceleration Equations The constant acceleration equations presented in this chapter are only applicable to situations in which the acceleration is constant. The most common mistake involving the constant acceleration equations is using them when the acceleration is changing. In chapter 6 we established that, by definition, dt d a v = (which we called equation 6-5) where a is the acceleration of an object moving along a straight line path, v is the velocity of the object and t , which stands for time, represents the reading of a stopwatch. This equation is called a differential equation because that is the name that we give to equations involving derivatives. Its true for any function that gives a value of a for each value of t . An important special case is the case in which a is simply a constant. Here we derive some relations between the variables of motion for just that special case, the case in which a is constant. Equation 6-5, dt d a v = , with a stipulated to be a constant, can be considered to be a relationship between v and t . Solving it is equivalent to finding an expression for the function that gives the value of v for each value of t . So our goal is to find the function whose derivative dt d v is a constant. The derivative, with respect to t , of a constant times t is just the constant. Recalling that we want that constant to be a , lets try: at = v Well call this our trial solution. Lets plug it into equation 6-5, dt d a v = , and see if it works....
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