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Below is a graph of the distance David traveled away from his home on a trip to the mountains. Place the events listed at right in the proper order based on details from the graph.

Trace the graph below and identify the parts that correspond to each event during David’s trip.

Then answer parts (a) through (d) below. 

The four places where events take place are the places where the slope changes: 
1) The spot where the graph flattens out momentarily.
2) The long horizontal section of the graph.
3) Where the slope is negative for a short time. 
4) Where the slope is negative for a long time.


  1. David has to drive back to pick up his credit card that he forgot at the restaurant.

  2. David’s car breaks down and he is towed back to a repair shop near his house.

  3. David stops for gas and gets a quick bite to eat.

  4. David gets pulled over and receives a speeding ticket. He then continues his trip at a slower rate.

First quadrant continuous curve, x axis labeled time, hours, y axis labeled distance from home, miles, starting at the origin, running right with slight increase, then rising almost vertically, then running almost horizontally, then rising almost vertically, then rising slowly for longer interval, then rising quickly, turning & decreasing at about the same curve, then turning & rising about the same curve, reaching maximum & turning then decreasing quickly to the x axis.

  1. What are the units for the slope of the curve?

  2. What is significant about the slope of the curve when David is stopped?

    moving forward → positive slope
    moving backward → negative slope 
    stopping → __________

  3. How does the slope of the curve tell you when David is speeding?

    If velocity is slope of the distance graph... so speeding would mean steep slope. Be mindful that speeding could mean steep-and-positive or steep-and-negative.

  4. Interpret the graph where the slope is negative. What is David doing then?

    Refer to the hint in part (b).