Math 311-01/02

2-13-2018

* [Velocity and acceleration problems]*

1. Find the velocity and acceleration vectors at for the curve with position function

Hence,

2. Find the velocity and acceleration vectors at for the curve with position function

Hence,

3. The position of a pepperoni stromboli at time t is

Find its velocity vector and its speed at .

The velocity at is

The speed is

4. A hot dog moves on a circular path given by

Show that its position and velocity vectors are always perpendicular.

The position is

The velocity is

Hence,

Since the dot product is 0, the vectors are perpendicular.

5. The acceleration vector for a doughnut is

Find the position function , if and .

Now , so

Hence,

Next,

Now , so

Hence,

* [Arc length problems]*

6. Find the length of the helix

7. Find the length of the curve

*Very little is needed to make a happy life. It is all within
yourself, in your way of thinking.* - *Marcus Aurelius*

Copyright 2018 by Bruce Ikenaga