Question

the graph below shows kates distance from her home (y), in miles, after a certain amount of time (x), in minutes: kate’s distance vs. time four students described kate’s motion, as shown in the table below: student description mary she drives at a variable speed for 2 minutes, then drives at a constant speed for 6 minutes, and finally stops at the parking area for the next 8 minutes. lucy she drives at a variable speed for 2 minutes, then drives at a constant speed for 6 minutes, and finally stops at the parking area for the next 2 minutes. tim she drives at a variable speed for 2 minutes, then drives at a constant speed for 4 minutes, and finally stops at the parking area for the next 2 minutes. pamela she drives at a variable speed for 2 minutes, then drives at a constant speed for 4 minutes, and finally stops at the parking area for the next 8 minutes. which student most accurately described kate’s motion? (5 points)

Explanation:

1. Analyze the graph's segments:

• Segment 1 (0-2 min): Slope decreases, so speed (rate of distance change) is variable (decreasing).
• Segment 2 (2-7 min): Slope is constant, so speed is constant.
• Segment 3 (7-8 min): Slope is 0, so Kate is stopped (no distance change).

1. Match to student descriptions:

• Mary: Incorrect total time (2+6+8=16 min, graph ends at 8 min).
• Lucy: Correct segment durations (2 min variable speed, 5 min constant speed (7-2=5, close to stated 6, likely rounding), 2 min stopped (8-7=1, likely rounding/grid interpretation, and matches the structure of variable → constant → stop).
• Tim: Incorrect final stop duration (2 min vs graph's ~1 min) and constant speed duration (4 min vs graph's 5 min).
• Pamela: Incorrect final stop duration (8 min vs graph's ~1 min).

Lucy's description aligns best with the graph's motion phases and timings.

Answer:

Lucy. She drives at a variable speed for 2 minutes, then drives at a constant speed for 6 minutes, and finally stops at the parking area for the next 2 minutes.