# Graph Sketching: Relating Distance and Velocity

See the design goals. See the matching Ontario Mathematics Curriculum expectations.

Elements to be fixed or checked:

- remove third checkbox from each gear ... also remove associated graphs
- check 2D plane video

- Consider the following:
- When riding a bike, how is the rate at which we pedal related to the speed of the bike?
- Describe how the pedal rate changes when you start from rest. Sketch a graph of the pedal rate vs. time.
- What happens physically when you change the gear on your bike from a lower gear to a higher gear?
- How does the timing of a gear change affect the velocity of the bike?

- Have the interactive start with no graphs on the screen. Move the control point of the gear change and watch the bikes race at the side of the graph. Try this several different times, and see the impact on the results of the race.
- View the distance graphs for each bike first. View them one at a time, and then together.
- How would you describe the distance graph for each bike?
- How are the graphs similar?
- How are the graphs different?
- How do you know from the graph which bike has won the race?
- After viewing the distance-time graphs for each bike, repeat the process for the velocity-time graphs.
- How would you describe the velocity graph for each bike?
- Where is each graph increasing/decreasing/constant?
- How are the graphs similar?
- How are the graphs different?
- How do you know from the graph which bike has won the race?

- For students in MCV 4U, there should be a discussion of the rate of change of each graph, as well as the distance graph being f(t), velocity as f’(t) and acceleration as f’’(t).