Motion Graph Match

Hook 5 min

1. Sketch a position graph that rises, stays flat, then falls. "Walk this graph." One student walks it in front of the room.
2. "A graph is not a picture of the path. Today you learn to read three graphs at once."

Explore 15 min

1. On the projector, drag the cart from 1 m to about 7 m and let go. "Why does the velocity graph make a bump? Why does acceleration go up, then down?"
2. Pairs pick Throttle, press Clear and push the slider to 1.0 m/s. "What does position do?" (Climbs 1 m every second.)
3. Pairs pick Pedal, press Clear and hold 0.2 m/s² for 5 s. They record velocity (1.0 m/s) and position (about 2.5 m). The force arrow reads 0.40 N.
4. Pairs let a run reach 12 s and turn on Show links.

Make sense 10 min

1. With Show links on, move across the graphs. The slope on each graph matches the value on the graph below it.
2. The shaded area under velocity matches the change in position. "Position is the running total of velocity."
3. Connect to F = m a: "The force arrow is 0.40 N with a 2.0 kg cart. What is the acceleration?"

Apply 15 min

1. Pairs switch to Race and pick a target card. Press Start and keep the line inside the shaded band.
2. Pairs try the same target with a different control. "Which control makes position targets easiest? Hardest? Why?"
3. Discuss target 6, Turnaround: "The cart stops for an instant at 3 s. Is the acceleration zero there?" (No: it is −0.5 m/s² the whole time.)
4. "Why can't a real cart follow target 1 exactly?" Press Show all three to see.

Exit check 5 min

On a card, sketch the velocity and acceleration graphs for this position graph: still for 2 s, then rising steadily for 4 s, then still. Then: "Where on a position graph is the velocity largest?" Velocity graphs with a ramp instead of a flat step show who needs Show links again.