Question

Graph the trajectory and find the velocity and speed.
An object moves on a path described by
r(t)= <8cost, 8sint> for 0<=t<=2Pi

Im assuming that the graph is basically a circle of a radius of 8. Then I would find x'(t) and y'(t)
in that the velocity would equal
v(t)= <-8sint, 8cost>
correct? and thus the speed would be 8m/s?

if that is correct then for these two would be done the similar way?

r(t)=<8cos3t, 8sin3t> for 0<=t<=2pi/3
r(t)=<8cos(sqrt), 8sin(sqrt)> for 0<=t<=(4pi)^2

they all have the same trajectory graph correct? just the velocities and speed are different?

Answer 1

Yes, all give you the same circle.