Question

The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph:

Part A: Is the graph linear or nonlinear? Explain your answer. (2 points)
Part B: In which segments is the graph increasing, decreasing, and constant? (3 points)
Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)

Answer 1

Part A

The graph is non-linear as it is not a continuous straight line (with only one slope).

Part B

Increasing: the y-value increases as the x-value increases

Constant: the y-value stays the same as the x-value changes

Decreasing: the y-value decreases as the x-value increases

Therefore,

• Increasing segment: Between 0 and 2 seconds
• Constant segment: Between 2 and 3 seconds
• Decreasing segment: Between 3 and 5 seconds

Part C

For the first 2 seconds, the ant moves 6 cm from a hole in the tree at a steady speed of 3 cm per second. For the next second, the ant is at rest then turns around. For the next 2 seconds, the ant moves 6 cm back to the hole at a steady speed of 3 cm per second. The ant then stops.