Question

For l(t)=(5sint, 5cost) describing the motion of a circle x^2+y^2=25, what would the velocity be at t=pi/3

Answer 1

Calculate the vector velocity: note that l(t) = (x(t),y(t)), then vector velocity
dl/dt = (dx/dt, dy/dt)

Answer 2

= magnitude of (5cos(t), -5sin(t))

Answer 3

= sqrt (25)= 5m/s

Answer 4

The questions asks for velocity, not speed.

Answer 5

5/2,-5sqrt(3)/2

Answer 6

Hm, velocity at t, v(t) = 5(cos t, -sin t).

So v(pi/3) = 5( cos(pi/3), -sin(pi/3))
= ...

Answer 7

Yes, you've got it.