Question: If an object moves along a parametric curve given by x = f(t) and y = g(t), its velocity at time t is the vector

If an object moves along a parametric curve given by x = f(t) and y = g(t), its velocity at time t is the vector v(t) given by v(t)=f(t), g(t)= f(t)i + g(t)j, and its speed at time t is the magnitude of the velocity, namely |v(t)|.(a) An object moving around the unit circle has position given by x = cos(t) and y = sin(t) at time t. Sketch the path of the object and mark its position (with a bold dot) at each of the times t=0,t=/2,t=,andt=3/2. Thenfindthevelocityoftheobjectateachofthosetimes. Why do these velocities make sense?

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