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(Solved): A particle is traveling on the unit circle. Its angular position \theta in terms of radians as a fun ...
A particle is traveling on the unit circle. Its angular position \theta in terms of radians as a function of time t is \theta =F(t), thus its
Cartesian coordinates are (x(t),y(t)), where x(t)=cos(F(t)) and y(t)=sin(F(t)). Assume that F(t) is a continuous,
differentiable function which increases with time (so the particle always is moving counterclockwise, it never backtracks). Let
f(t) be the derivative of F(t). The length of the path that the particle follows from t=0 to t=1 is given by an integral of the
form \int_0^1 g(t)dt.
(a) What is the integrand, g(t) ?
(b) Assume that F(0)=1 and that F(1)=7. What is the length of the path?