# Mechanics

calculus-based physics for scientists and engineers

## Uniform Motion: motion with zero acceleration

### Uniform Motion

Uniform motion is the special case where the acceleration is zero. The various functions are:
•   function
• $$a(t)$$
• $$v(t)$$
• $$x(t)$$
•   expression
• $$0$$
• $$v$$
• $$x_o+vt$$
•   information
• zero
•   constant, some fixed number
• $$x_o$$ is the initial position, $$x(0)$$

### Solving Uniform Motion Problems

When solving uniform motion problems we are usually interested in an event between two points in time we'll call $$t_i$$ and $$t_f$$, the initial time and the final time. In this case we introduce the notation for the initial and final position: $$x_i = x(t_i)=x_o+vt_i$$ $$x_f = x(t_f)=x_o+vt_f$$ Note that $$\Delta t = t_f-t_i$$ and $$\Delta x = x_f-x_i = v\Delta t$$. This gives us a useful relationship between the initial and final position: $$x_f = x_i + v\Delta t$$ Now is the time to start using (even if you don't specifically need to) the problem solving strategy. Review the module on this if necessary. Some tips:
1. Make sure you have large amounts of blank scratch paper.
2. Draw a picture.
3. Draw a schematic diagram with a coordinate system with a well-defined zero and positive direction
4. Find and list what you know and what you need to know.
5. Determine what physics applies to the problem and find relationships between what you know and don't know.
6. If you have the same number of independent equations and unknowns you should be able to solve the problem.
7. For more than one object add numbered subscripts (1, 2, etc.) to distinguish between objects.

### Solution

1. Bob is a slow and fat physics professor that runs at a top speed of 6 m/s when chased by a velociraptor running at a top speed of 31 m/s. If Bob has a 100 m head start, how far does he get before he is caught and devoured?