Unformatted text preview: F in moving from x to x 1 . In the case that F is the force of gravity exerted by the earth, it is customary to make F < 0 since the force is “downward.” This makes the work W negative when it should be positive, so typically the work in this case is deﬁned as W =Z x 1 x F dx. Also, by Newton’s Law, F = ma ( t ). This means that W =Z x 1 x ma ( t ) dx. Unfortunately this integral is a bit problematic: a ( t ) is in terms of t , while the limits and the “ dx ” are in terms of x . But x and t are certainly related here: x = x ( t ) is the function that gives the position of the object at time t , so v = v ( t ) = dx/dt = x ± ( t ) is its velocity...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Improper Integrals, Integrals, Energy, Force, Potential Energy, Cauchy principal value

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