Chapter 0.4, Problem 35E

(a)

To determine

To calculate : The parameterizations to model the motion of a particle.

Answer to Problem 35E

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once clockwise is $x=a\cos t,y=-a\sin t,0\le t\le 2\pi$ .

Explanation of Solution

Given information :

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once clockwise.

Calculation:

For once clockwise motion of the particle time will be $0\le t\le 2\pi$ .

At $t=\frac{\pi }{2}$ , the particle will be at $\left(0,-a\right)$ and at $t=\pi$ , the particle will be at $\left(-a,0\right)$ .

Therefore, the parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once clockwise is $x=a\cos t,y=-a\sin t,0\le t\le 2\pi$ .

(b)

To determine

To calculate : The parameterizations to model the motion of a particle.

Answer to Problem 35E

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once counter clockwise is $x=a\cos t,y=a\sin t,0\le t\le 2\pi$ .

Explanation of Solution

Given information :

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once counter clockwise.

Calculation:

For once counter clockwise motion of the particle time will be $0\le t\le 2\pi$ .

At $t=\frac{\pi }{2}$ , the particle will be at $\left(0,a\right)$ and at $t=\pi$ , the particle will be at $\left(-a,0\right)$ .

Therefore, the parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces

Therefore, the parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once clockwise is $x=a\cos t,y=a\sin t,0\le t\le 2\pi$ .

(c)

To determine

To calculate : The parameterizations to model the motion of a particle.

Answer to Problem 35E

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ twice clockwise is $x=a\cos t,y=-a\sin t,0\le t\le 4\pi$ .

Explanation of Solution

Given information :

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ twice clockwise.

Calculation:

For twice clockwise motion of the particle time will be $0\le t\le 4\pi$ .

Therefore, the parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ twice clockwise is $x=a\cos t,y=-a\sin t,0\le t\le 4\pi$ .

(d)

To determine

To calculate : The parameterizations to model the motion of a particle.

Answer to Problem 35E

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ twice counter clockwise is $x=a\cos t,y=a\sin t,0\le t\le 4\pi$ .

Explanation of Solution

Given information :

The parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ twice counter clockwise.

Calculation:

For once counter clockwise motion of the particle time will be $0\le t\le 4\pi$ .

Therefore, the parameterizations to model the motion of a particle that starts at $\left(a,0\right)$ and traces the circle $x^2+y^2=a^2,a>0$ once clockwise is $x=a\cos t,y=a\sin t,0\le t\le 4\pi$ .