Answer
a) The proof is below.
b) $\vec{v}=\omega A cos(\omega t)\hat{i}+\omega Asin(\omega t)\hat{j}$
c) $\omega A$
d) $\omega$
Work Step by Step
a) We factor to find:
$\vec{v}= A((cos\omega t)\hat{i}-sin(\omega t )\hat{j})$
We see that this is a circle, so we see that there is a constant distance of $A$.
b) We take the derivative of position to find the velocity:
$\vec{v}=\omega A cos(\omega t)\hat{i}+\omega Asin(\omega t)\hat{j}$
c) The magnitude of the velocity vector is equal to the value of what the whole vector is multiplied by, which is $\omega A$.
d) We see that the object's angular speed is $\omega$ using the original equation.
