Chapter 10.3, Problem 73E

(a)

To determine

To-graph: Two sets of parametric equations with the use of graphing utility. First set of parametric equations are $x=t-\sin t$ and $y=1-\cos t$ over the interval $\left[0,2\pi \right]$. And, the second set of parametric equations are $x=2t-\sin \left(2t\right)$ and $y=1-\cos \left(2t\right)$ over the interval $\left[0,\pi \right]$.

(b)

To determine

To calculate: The inference about the average speeds of the particle on the paths represented by the two set of parametric equations in part (a).

(c)

To determine

To calculate: The time required for a particle to traverse the same path as in parts (a) and (b) when the path is modelled by $x=\frac{1}{2}t-\sin \left(\frac{1}{2}t\right)$ and $y=1-\cos \left(\frac{1}{2}t\right)$.