Question

1. sketch the graph, then answer the question below. a. kyler starts 2 feet away from the motion detector. b. he then walks away from the motion detector at a rate of 2 feet per second for 2 seconds. c. he remains still for 2 seconds. d. he then walks toward the motion detector at a rate of - 1/3 ft/sec for 6 seconds. how far is kyler from the motion detector when he finishes his walk? kyler is 8 ft ft away from the motion detector when he finishes.

Explanation:

Step1: Analyze part a

Kyler starts 2 feet away. For 2 seconds, he moves away at a rate of 2 feet per second. The distance - time relationship for this part is a linear function with a positive slope. The distance $d_1$ from the detector after 2 seconds is $d_1=2 + 2\times2=6$ feet.

Step2: Analyze part b

He then walks away for 2 seconds at a rate of 2 feet per second. The distance $d_2$ from the detector after these 2 seconds is $d_2=d_1+2\times2=6 + 4 = 10$ feet.

Step3: Analyze part c

He remains still for 2 seconds. The distance from the detector does not change, so the graph is a horizontal line for these 2 seconds.

Step4: Analyze part d

He walks towards the detector at a rate of $\frac{1}{3}$ ft/sec for 6 seconds. The distance he covers is $d_3=\frac{1}{3}\times6 = 2$ feet. So the final distance $d$ from the detector is $d = 10-2=8$ feet.

Answer:

Kyler is 8 feet from the motion - detector when he finishes his walk.