[Velocity and acceleration problems]
1. Find the velocity and acceleration vectors at for the curve with position function
2. Find the velocity and acceleration vectors at for the curve with position function
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
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
Now , so
[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
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