## 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:

- Make sure you have large amounts of blank scratch paper.
- Draw a picture.
- Draw a schematic diagram with a coordinate system with a well-defined zero and positive direction
- Find and list what you know and what you need to know.
- Determine what physics applies to the problem and find relationships between what you know and don't know.
- If you have the same number of independent equations and unknowns you should be able to solve the problem.
- For more than one object add numbered subscripts (1, 2, etc.) to distinguish between objects.
- Always check to see if your answer makes sense.

### Exercises

*Do Now!* Do these exercises immediately.

*Not Now!* Do these after you start to forget the topic, say in a week.

*More!* More exercises if you want. Maybe review before a test.

### Required Problems

### 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?