The coordinates of an object moving in the xy plane vary with time according to

Question

The coordinates of an object moving in the xy plane vary with time according to the equations x = -5.43 sin omega t and y = 4.00 - 5.43 cos omega t, where omega is a constant, x and y are in meters, and t is in seconds. Determine the components of velocity of the object at t = 0. (Use the following as necessary: omega.) v = m/s Determine the components of the acceleration of the object at t = 0. (Use the following as necessary: omega.) a = m/s2 Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following as necessary: omega for omega and t.) r = m v = m a = m Describe the path of the object in an xy plot.

Explanation / Answer

x=-5.43sint

y=4-5.43cost

V=x'+y'=-5.43..cost.i+5.43..sint.j

=-5.43i+0=-5.43i => 5.43m/s2 opposite direction

a=x"+y"=5.43.2.sint.i+5.43.2.costj

=5.43.2j =>5.432 m/s2

r=-5.43sinti+(4-5.43cost)j

sint=(x/-5.43)

cost=(y-4)/5.43

squaring and addind:

1=(x/-5.43)2+[(y-4)/5.43]2

5.432=x2+(y-4)2

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