When a car rolls up and down a ramp, what do the distance and velocity graphs look like?

• Toy car that rolls easily
• Cardboard ramp about 50 cm long
• ITSI Probe kit motion sensor
• Extra cardboard
• Hot melt gluegun

Suppose you give a push to a cart at the bottom of a ramp. It rolls up the ramp, slows down, and then rolls back down. What would the graph of distance vs time look like?

Predict the shape of this graph. Imagine that you are measuring distance from the top of the ramp, so that distance decreases as the car goes up the ramp.

Now set up a real car, ramp, and motion detector.

• Use the ITSI Probe kit to build a motion sensor with an electric motor and a cardboard wheel. The building process is described in ITSI Activity 427
• Find a toy car that rolls very easily. It cannot be self-propelled with springs or a motor!
• Attach the motor a wheel assembly to the car with a cardboard ‘arm’.

• Make a cardboard ramp about 15×50 cm and set up one end on book. Tape down the other end to the table.
  
  

• Start the motion sensor. Hold the wires loosely so that the car is free to roll.
• Give the car a push up the ramp. Let it coast to a stop and coast down the ramp again. Catch it at the bottom. Note: if the graph is ‘upside down’, you can reverse the direction of increasing distance by switching the two wires to the motor.
• On your data graph, add labels describing what is happening during each part of the graph. Mark the points when the car starts coasting, when it reverses direction, and when it returns to the bottom of the ramp.

How good was your prediction? What was different about the real measurement? Was there any feature of the graph that surprised you?

Collect data: velocity graph

Suppose you did the same experiment but graphed velocity of the cart instead of distance.

• Predict the shape of this graph in the Prediction Graph above. Imagine that you are measuring velocity from the top of the ramp, so that velocity is negative as the car goes up the ramp and positive as the car goes down the ramp.
  Now do the same experiment, but graph velocity vs time instead of distance vs time. Note: if the graph is ‘upside down’, you can reverse the direction of increasing distance by switching the two wires to the motor.
• On your data graph, mark the points when the car starts coasting, when it reverses direction, and and when it returns to the bottom of the ramp.
• How can you tell from the graph at what point the car stops and reverses direction?

How good was your prediction? What was different about the real measurement? Was there any feature of the graph that surprised you?

• Explain the relationship between a distance vs time graph and a velocity vs time graph.
• How could How would you predict the velocity graph if you knew the shape of the distance graph?
• How would you predict the distance graph if you knew the shape of the velocity graph?

• Set the ramp at different angles. How does this change the graph?
• Graph the car coasting to a stop on a level surface. Can you predict the graph of a car coasting to a stop on a level surface? Try predicting, and then try the experiment.