Answer: Cycloidal Motion The figure shows the path of a particle modeled by the

Chapter 12, Problem 71

(choose chapter or problem)

Cycloidal Motion The figure shows the path of a particle modeled by the vector-valued function

\(\mathbf{r}(t)=\langle\pi t-\sin \pi t, 1-\cos \pi t\rangle\)

The figure also shows the vectors v(t)/||v(t)|| and a(t)/||a(t)|| at the indicated values of t

(a) Find \(a_{\mathrm{T}} \text { and } a_{\mathrm{N}}\) at \(t=\frac{1}{2}, t=1, \text { and } t=\frac{3}{2}\)

(b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. Give reasons for your answers.

Text Transcription:

r(t)= langle pi t-sin pi t, 1-cos pi t rangle

a_T

a_N

t=1/2

t=1

t=3/2