each curve represents the motion of a particle moving in R2
x(t) = (2cos t, 3sin t) , 0 <= t <= 2Pi
x(t) = (3 sec t, 2 tan t) , (-1/3)pi <= t <= (1/3)pi
can someone sketch both these curves showing the direction of motion for me???
and find the velocity and speed of each of the particles with a step by step explanation
the speed of the first one i got as:
sqrt ( 4(sin t)^2 + 6 (cos t)^2 )
is there any way to further simplify this or should i leave it like this???
i also have to locate the points (x,y) where the velocity is horizontal, vertical or 0
i think this means when the derivative or x-component is 0, when derivative or y-component is 0, and when both are zero?
am i correct?
and can you list those points for both equations as well so i can verify them