Solution Found!
Explain why or why not Determine whether the
Chapter 11, Problem 35E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. If an object moves on a trajectory with constant speed S over a time interval \(a \leq t \leq b\), then the length of the trajectory is S(b - a).
b. The curves defined by \(\mathbf{r}(t)=\langle f(t), g(t)\rangle\) and \(\mathbf{R}(t)=\langle g(t), f(t)\rangle\) have the same length over the interval [a, b].
c. The curve \(\mathbf{r}(t)=\langle f(t), g(t)\rangle \text { for } 0 \leq a \leq t \leq b\) band the curve \(\mathbf{R}(t)=\left\langle f\left(t^{2}\right), g\left(t^{2}\right)\right\rangle \text { for } \sqrt{a} \leq t \leq \sqrt{b}\) have the same length.
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. If an object moves on a trajectory with constant speed S over a time interval \(a \leq t \leq b\), then the length of the trajectory is S(b - a).
b. The curves defined by \(\mathbf{r}(t)=\langle f(t), g(t)\rangle\) and \(\mathbf{R}(t)=\langle g(t), f(t)\rangle\) have the same length over the interval [a, b].
c. The curve \(\mathbf{r}(t)=\langle f(t), g(t)\rangle \text { for } 0 \leq a \leq t \leq b\) band the curve \(\mathbf{R}(t)=\left\langle f\left(t^{2}\right), g\left(t^{2}\right)\right\rangle \text { for } \sqrt{a} \leq t \leq \sqrt{b}\) have the same length.
ANSWER:Solution 35EStep 1:Suppose an object moves in a space with a position function r(t)= then the distance traveled between t=a and t= b is given by