Question

a driver runs over a nail, puncturing the tire without causing a leak. the position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table.

time (s)	approximate height of the nail off the ground (inches)
0.01	2.1
0.02	7.6
0.03	14.9
0.04	21.5
0.05	25.5
0.06	25.5
0.07	21.5

which key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?

• period
• minimum
• maximum

Explanation:

The nail's motion as the tire rotates is periodic (since the tire is a circle, its rotation repeats). The period of a periodic function is the time it takes for the function to repeat its values (i.e., return to the same state/ orientation). The "minimum" is the lowest height, and "maximum" is the highest, but neither tells the time to return to the same orientation. Only the period represents the time for one full cycle (returning to the same orientation).

Answer:

A. period