Suppose the $\mathrm{x}$-position of an oscillating object is given by $x(t)=A \cos (\omega t+\theta)$. What is the object's speed at time $\mathrm{t}=0$ ?
A) $A$
B) Zero
C) $|A \cos \theta|$
D) $|A \sin \theta|$
E) $|A \omega \sin \theta|$
F) Something else (specify)
G) We are not given enough information to answer.

Question

Quizplus · Accepted Answer

The speed of the object is the magnitude of the derivative of its position with respect to time. Differentiating $x(t)=A \cos (\omega t+\theta)$ with respect to $t$ gives the velocity $v(t) = -A\omega \sin(\omega t + \theta)$. At $t=0$, $v(0) = -A\omega \sin(\theta)$, and the speed, being the magnitude of velocity, is $|A\omega \sin(\theta)|$.

Suppose The x\mathrm{x}x -Position of an Oscillating Object Is Given By x(t)=Acos⁡(ωt+θ)x(t)=A \cos (\omega t+\theta)x(t)=Acos(ωt+θ)

Suppose The $\mathrm{x}$ -Position of an Oscillating Object Is Given By $x(t)=A \cos (\omega t+\theta)$