Essential University Physics: Volume 1 (3rd Edition)

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) $\omega$
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.