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 following equations. t is in seconds and w has units of radians*seconds -1.
x = -(5.00 m) sin wt

y = (4.00 m) - (5.00 m) cos wt
(a) Determine the components of velocity and components of acceleration at t = 0. (Use omega for w.)
v= ( i+ j) m/s
a= ( i+ j) m/s2

(b) Write expressions for the position vector, the velocity vector, and the acceleration vector at any time t > 0. (Use omega for and t as appropriate.)
r= ( i+ j ) m
v= ( i+ j ) m/s
a= ( i+ j ) m/s2

(c) Describe the path of the object on an xy graph.

Explanation / Answer

v= dx/dt i + dy/dt j = -5w cos wt i + 5w sin wt j t= 0, ==> V= 5w i +0j A= d2x/dt2 i + d2y/dt2 j = 5w^2 sinwt i + 5w^2 coswt j t= 0 ==> a= 5w^2 j + 0i b. r= [-(5.00 m) sin wt ]i +[ (4.00 m) - (5.00 m) cos wt ] j V= -5w cos wt i + 5w sin wt j A= 5w^2 sinwt i + 5w^2 coswt j the path followed is a ellipse.

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