Staring from the pit, Helen made three laps around a circular track at 40 seconds per lap. She than made a 30-second pit stop and two and a half laps before running off the track and getting stuck in the mud for the remainder of the race. Graph Helen's distance from the pit as a function of time.
To graph Helen's distance from the pit as a function of time, we need to understand her movement on the track and during the pit stop.
First, let's break down her movement on the track:
- Helen completed three laps around the circular track. Each lap takes 40 seconds, so she spent 3 x 40 = 120 seconds running on the track (not including the pit stop).
- After the third lap, she made a 30-second pit stop.
Next, let's analyze her movement after the pit stop:
- She made two and a half laps, but then ran off the track and got stuck in the mud.
To graph her distance from the pit over time, we can divide her race into several segments and calculate her distance during each segment. Let's go step by step:
1. Initial position at the pit: Her distance is zero at the start.
2. First three laps on the track: Helen covers a distance of 3 laps x circumference of the circle track.
3. Pit stop: During the 30-second pit stop, Helen's distance remains the same.
4. Two and a half laps after the pit stop: Calculate the distance covered by Helen in two full laps plus half of the distance of a lap.
5. Getting stuck in the mud: Once Helen gets stuck in the mud, her distance remains constant.
Now, we have divided Helen's race into different segments. To graph her distance from the pit as a function of time, we can plot these segments on a graph:
- On the x-axis, represent time in seconds.
- On the y-axis, represent Helen's distance from the pit.
Using this information, you can plot the graph step by step, starting from zero distance at the pit and extending it according to her distance covered at each segment.