Question

beverly and carl are in a race. their graphs show the data. 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 beverlys. even though for a majority of the race they accelerated at the same rate, beverly won because her initial acceleration was greater than carls. beverly accelerated at a greater rate for the entire race. carl accelerated at a greater rate for the entire race.

Explanation:

1. Analyze the slope (acceleration, since acceleration = change in velocity / change in time) of the velocity - time graphs:

• The slope of a velocity - time graph represents acceleration. For the initial part (before around 10 seconds), Beverly's graph has a steeper slope than Carl's, meaning her initial acceleration was greater.
• After around 10 seconds, the slopes of their graphs (the rate of change of velocity) seem to be the same (the lines are parallel).
• To determine who won, we can think about the distance covered (area under the velocity - time graph). Since Beverly had a greater initial acceleration and then the same acceleration as Carl for the rest of the race, she would cover more distance.

1. Evaluate each option:

• Option 1: Says Carl won because initial acceleration was greater, but Beverly's initial slope (acceleration) is steeper, so this is wrong.
• Option 2: Says that for a majority of the race they accelerated at the same rate (parallel lines after 10 seconds) and Beverly won because her initial acceleration was greater (steeper initial slope), which matches our analysis.
• Option 3: Beverly did not accelerate at a greater rate for the entire race (after 10 seconds, slopes are equal), so this is wrong.
• Option 4: Carl did not accelerate at a greater rate for the entire race (Beverly's initial slope is steeper and then slopes are equal), so this is wrong.

Answer:

B. 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.