You are a single bacterium living on a microscope slide. There is a glucose (or other nutrient) deposit 30 micrometers to your right. Unfortunately, you can only take 20 micrometer steps. You must end your step on the glucose deposit to eat it. What directions can you take these steps in to get to your food?

1. What is the change in velocity (magnitude and direction) each time you change direction?
2. Now suppose that you are limited in how much you canchangeyour velocity(v=v2v1). You start off with 20 micrometer steps, but each subsequent step can only be different by a small v. How does this limit your motion? What paths to the glucose are going to be quickest under these constraints? You don't need numbers for this part.