Question

shelby is swimming laps at greengate pool. she starts in her lane at one end of the pool and swims her first back-and-forth lap using the butterfly stroke. then, she does one slower lap of the backstroke. which graph could show shelbys distance from her starting position over time? four graphs are shown with distance from start (m) on y - axis and time (sec.) on x - axis, each with a green line graph representing distance over time

Explanation:

Step1: Analyze initial position

Shelby starts at the starting position, so at time \( t = 0 \), distance from start is \( 0 \). This eliminates graphs where \( y\)-intercept is non - zero (like the top - right and bottom - right graphs which start at a non - zero distance).

Step2: Analyze speed for each lap

• First lap (butterfly stroke): A back - and - forth lap. The time taken for this lap will be less than the second lap (backstroke) since backstroke is slower. In a distance - time graph, a steeper line means higher speed (since speed \(=\frac{\text{distance}}{\text{time}}\), for the same distance, less time means steeper slope).
• Second lap (backstroke): Slower, so the time taken for the back - and - forth lap is more, so the slope of the line (for distance vs time) will be less steep compared to the first lap.
• Looking at the remaining graphs (top - left and bottom - left):
• The top - left graph: The first peak (first lap) and the second peak (second lap) have the same "width" (time taken for the lap), which would imply same speed, so it's incorrect.
• The bottom - left graph: The first lap (first peak) has a steeper slope (less time taken) and the second lap (second peak) has a less steep slope (more time taken) as the "width" of the second peak (time for the lap) is wider than the first, which matches the fact that backstroke is slower. Also, it starts at \( (0,0) \).

Answer:

The bottom - left graph (the third graph in the order, or the graph in the bottom - left corner)