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 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.

Explanation:

1. Analyze the velocity - time graph: The slope of a velocity - time graph represents acceleration.
2. Initial part (before around 10 seconds): Beverly's velocity - time graph has a steeper slope than Carl's, so Beverly's initial acceleration is greater.
3. After around 10 seconds: The slopes of both graphs are the same (parallel lines), meaning their acceleration is the same for the majority of the race.
4. Since Beverly had a greater initial acceleration and then same acceleration as Carl for most of the race, she would cover more distance (area under the velocity - time graph) and win the race.
5. Eliminate other options:

• Option 1 is wrong because Carl did not have greater initial acceleration.
• Option 3 is wrong as their acceleration was same after the initial part.
• Option 4 is wrong as Beverly had greater initial acceleration and same acceleration later.

Answer:

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.