Question

Beverly and Carl are in a race. Their graphs show the data.

A graph with horizontal axis time (seconds) and vertical axis velocity (meters per second). An orange line labeled Beverly starts at 0 seconds 0 meters and goes straight to 10 seconds 15 meters and then to 50 seconds 35 meters. A blue line labeled starts at 0 seconds 0 meters and goes straight to 10 seconds 10 meters and then to 50 seconds 30 meters.

Which best describes the race?

Even though for a majority of the race they accelerated at the same rate, Carl won because his initial acceleration was greater than Beverly’s.
Even though for a majority of the race they accelerated at the same rate, Beverly won because her initial acceleration was greater than Carl’s.
Beverly accelerated at a greater rate for the entire race.
Carl accelerated at a greater rate for the entir

Answer 1

"Even though for a majority of the race they accelerated at the same rate, Beverly won because her initial acceleration was greater than Carl’s."

Reason: From 0–10 s Beverly’s acceleration = (15–0)/10 = 1.5 m/s², Carl’s = (10–0)/10 = 1.0 m/s². From 10–50 s both accelerate at (35–15)/40 = (30–10)/40 = 0.5 m/s². Distance = area under v–t curve: Beverly = 75 + 1000 = 1075 m; Carl = 50 + 800 = 850 m. Beverly covers more distance, so she wins.