An object moves in the x-y plane with coordinates given as a function of time by: x(t) = R cos(ωt) y(t) = R sin(ωt) where R and ω are constants. What is the velocity vector of the object at any time t?
Added by Richard H.
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Step 1:** The velocity along the x-axis is given by the derivative of x with respect to time: \[ \frac{dx}{dt} = -R\omega \sin(\omega t) \] ** Show more…
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The coordinates of an object moving in the $x y$ plane vary with time according to the equations $x=-(5.00 \mathrm{m}) \sin (\omega t)$ and $y=(4.00 \mathrm{m})-(5.00 \mathrm{m}) \cos (\omega t),$ where $\omega$ is a constant and $t$ is in seconds. (a) Determine the components of velocity and components of acceleration at $t=0 .$ (b) Write ex- pressions for the position vector, the velocity vector, and the acceleration vector at any time $t>0 .$ (c) Describe the path of the object in an $x y$ plot.
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