Question

summarize it!

1. construct and present arguments a distance - time graph shows the motion of two bicycle riders. each rider’s motion is represented on the graph by a diagonal line sloping upward from left to right. the graph shows that they traveled the same distance. however, the line representing the motion of rider #1 slopes upward more steeply than the line representing the motion of rider #2. sketch a graphical model of the motions of the riders. develop an argument on which rider arrived at his or her destination first. how do you know? use evidence to add validity to your argument.

Explanation:

1. Graphical Model: On a distance-time graph, plot the y-axis as distance and x-axis as time. Draw two upward-sloping diagonal lines starting from the origin (0,0) that end at the same y-value (equal total distance). The line for Rider #1 will be steeper than the line for Rider #2.
2. Argument: The slope of a distance-time graph equals speed ($\text{speed} = \frac{\text{distance}}{\text{time}}$). A steeper slope means higher speed. Since both riders travel the same distance, the faster rider (Rider #1) will take less time to reach the destination. This is confirmed by the graph: Rider #1's line reaches the final distance at a smaller x-value (time) than Rider #2's line.

Answer:

1. Graphical Sketch:

• Axes: x-axis = Time, y-axis = Distance
• Rider #1: Steep diagonal line from (0,0) to $(t_1, D)$ where $t_1$ is a smaller time value
• Rider #2: Less steep diagonal line from (0,0) to $(t_2, D)$ where $t_2 > t_1$

1. Conclusion: Rider #1 arrived at the destination first. This is because the steeper slope of Rider #1's line indicates a higher constant speed, and covering the same distance at a higher speed requires less time, as shown by the smaller time value on the x-axis when reaching the shared final distance.