The coordinates of an object moving in the xy plane vary with time according to the equations x = -6.85 sin ωt and y = 4.00 - 6.85 cos ωt, where ω is a constant, x and y are in meters, and t is in seconds.

Question

The coordinates of an object moving in the xy plane vary with time according to the equations x = -6.85 sin ωt and y = 4.00 - 6.85 cos ωt, where ω is a constant, x and y are in meters, and t is in seconds.
a. Determine the components of the velocity of the object at t = 0.
b. Determine the components of the acceleration of the object at t = 0.
c. Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0.
d. Describe the path of the object in an xy plot.

@oobleck · Accepted Answer

you say clearly but then Don’t explain why.

oobleck · Answer

dx/dt = -6.85ω cosωt
dy/dt = 6.85ω sinωt
do that again for acceleration, and evaluate at t=0
clearly, the path is a circle with center at (0,4) and radius r=6.85, traced clockwise starting at (0,-2.85)