Answer
The answers are below.
Work Step by Step
a) We know the following equation for a position on a circle:
$cos\theta \hat{i} +sin\theta \hat{j}$
To specify for a specific circle, we multiply by the radius, giving:
$\vec{r}=R(cos\theta \hat{i} +sin\theta \hat{j})$
b) We know that the percentage of the cycle it will have completed at any point is equal to $\frac{t}{T}$. Multiplying this by 360, we find that the value of theta, in degrees, is:
$\theta = \frac{360t}{T}$
c) The second derivative is:
$=R(-cos\theta \hat{i} -sin\theta \hat{j})$
Based on the negatives, we see that the direction is toward the center of the circle. In addition, we know that the magnitude of an acceleration vector is $\frac{v^2}{R}$.
