A)
B)
C)
D)
Correct Answer: D
Solution :
Based on the description of the particle?s position at time \[t=0,\] we know that the equation that describes the particle?s x-coordinate as a function of time is \[x=A\cos (\omega t)\] To determine the x-component of the velocity, we take the time derivative of this function: \[{{v}_{x}}=\frac{dx}{dt}=\frac{d}{dt}A\,\,\cos (\omega t)=-\,\omega A\,\,\sin \,\,(\omega t)\] This is essentially a negative sine function, which matches the graph in answer 4. The problem may be solved conceptually, too, by considering the x-component of the rotating particle as a mass on a horizontally-stretched spring. The mass is released from a position +A at time t=0, at which point it begins to accelerate in the x-direction, beginning a simple harmonic oscillation. This motion is consistent with answer.
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