### How to make sure that what your friend claims is true

In a position-time graph for constant velocity. the position changes by the same amount in every time interval. This means that if you were to start out at 0 meters and by 1 second, you are at 1 meter, then you would increase by 1 meter every second onwards. On a graph, it means that the graph would have the same slope throughout (a linear function).

For example, your friend walks to school everyday and claim that he is always walking at the same speed. You, however, are extremely skeptical of everything. One day, you decided to walk with your friend to school carrying a ruler, a pen, and a stopwatch. Every five seconds, you would mark off the start and end positions of your friend and measure the distance.

### Creative Applications

1. What must be true about the data (not the graph) in order to show that your friend actually does walk at the same speed all the way to school?

2. What must be true about the graph in order to show that your friend actually does walk at the same speed all the way to school?

3. Let’s say that from your graph, you see curves going up and down. What conclusion would you make and what would you say to your friend?