3. (8 pts) Trajectory of a particle. A particle moves in a two-dimensional orbit

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3. (8 pts) Trajectory of a particle. A particle moves in a two-dimensional orbit de?ned by
x(t) = ro0[1 + cos(omegat)] (1)
y(t) = ro0[2 + sin(omegat)] (2)
(a) Sketch the trajectory. Find the velocity and acceleration (as vectors, and also their magnitudes), and draw the corresponding velocity and acceleration vectors along various points of your trajectory. Discuss the results physically - can you relate your ?nding to what you know from previous courses? Finally: what would you have to change if you want the motion to go the other way around?

(c) Prove (in general, not just for the above situation) that if velocity, v(t), of any particle has constant magnitude, then its acceleration is orthogonal to v(t). Is this result valid/relevant for the trajectorydiscussed in part a?
Hint There’s a nice trick here - consider the time derivative of |v(t)|^2=v.v

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