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 entire race.

Answer 1

Option 2.

Reason: Acceleration = slope of v–t. From 0–10 s Beverly’s a = (15−0)/10 = 1.5 m/s², Carl’s a = (10−0)/10 = 1.0 m/s². From 10–50 s both have a = (35−15)/40 = (30−10)/40 = 0.5 m/s², so they accelerate the same for the majority of the race. Area under each v–t curve (distance): Beverly = 0.5·10·15 + 40·((15+35)/2) = 75 + 1000 = 1075 m; Carl = 0.5·10·10 + 40·((10+30)/2) = 50 + 800 = 850 m. Beverly covers more distance, so she wins.