Car on an Incline
Activity 2
Download the answer log for this activity.
Investigation 1
Scenario 1
Carolyn has a remote control car. With the controls, she can decide how much power she gives the car. On a flat surface, if she keeps the power at the same level, the car gets faster and faster.
After playing with the car on the flat street, Carolyn decided to send the car up the part of the street that goes up a hill as shown in the picture below. If she didn't give the car enough power, it eventually stopped and then rolled back down the hill. (You may recall seeing this happen with a toy car in the previous lesson.)
This picture shows Carolyn's car when she gave it a power of 10 and its forward speed up the hill was 3 feet per second. The car is shown when it first touched the hill (0 seconds), 0.5 second later, and 1 second after it first touched the hill. The height of the car above the flat street is given.
The following
interactive graph also shows how the car's height changed over time. The horizontal
axis shows time in seconds, and the vertical axis shows the height in
feet. (For example, Point A shows that 0.5 second after the car starts up the
ramp, the car is 0.47 feet off the ground.) The points on the graph are placed
at half-second intervals.
Beside the table of time and height values is a list of
height differences, which shows the difference in height from one point to the
next.
1.
Leave the power setting at 10 and the initialSpeed at 3. Click on the dot on the time slider, then use the arrow keys
to move the slider to 1 second. Watch the red point as you move the slider from
1 second to 1.5 seconds. Then move the time slider to 4 seconds, and watch
the red point as you move the slider from 4 seconds to 4.5 seconds.
Compare the differences from 1
second to 1.5 seconds, and from 4 seconds to 4.5 seconds. Use the graph and the
movement of the red point to help you decide what a positive difference means
and what a negative difference means.
2.
For a moment, ignore the signs of the differences and just
look at the size of the rest of the number. Find a pattern in the list of
differences and compare that pattern to the shape of the graph. How is the way
the differences change connected to the shape of the graph?
Continue to Investigation 2.
EDC, Created with GeoGebra