Assume a smooth curve C is described by the vector function r(t) for a :5 t :5 b. Let
Chapter 9, Problem 39(choose chapter or problem)
Assume a smooth curve C is described by the vector function r(t) for a :5 t :5 b. Let acceleration, velocity, and speed be given by a = dvldt, v = drldt, and v = II vii , respectively. Using Newton's second law F = ma, show that, in the absence of friction, the work done by F in moving a particle of constant mass m from point A at t = a to point B at t =b is the same as the change in kinetic energy: K(B) - K(A) = 2 m[(vb)]2 - 2 m[(va)]2 [Hint: Consider : t v2 = : t v v. ]
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