Question

four friends ran a 10k race and finished 1, 2, 3, and 4.
what occurred with runner bs line in the graph?
a runner b came in second with a burst of speed at the end.
b runner b passed runner c with a burst of speed at the end when runner c slowed.
c runner b had a constant speed for half the race, then quickly accelerated past runner c at the end.
d runner b had the same acceleration as all three runners, but almost toward the end, he put on a burst of speed to pass runner c.

Explanation:

Step1: Analyze the graph

The graph shows the distance - time relationship for four runners. The slope of the distance - time graph represents speed. A steeper slope means a higher speed.

Step2: Evaluate each option

• Option A: If Runner B had a burst of speed at the end, its slope (speed) should increase at the end. But in the graph, Runner B's slope does not show a significant increase at the end.
• Option B: If Runner B passed Runner C with a burst of speed when Runner C slowed, there should be a point where the slope of Runner B's graph becomes steeper than Runner C's graph. In the graph, we can see that at the end, Runner B's graph (which has a relatively flat slope initially) has a steeper slope than Runner C's graph (which has a very flat slope at the end).
• Option C: If Runner B had a constant speed for half the race and then accelerated, the graph should have a part with a constant slope (for the constant - speed part) and then a steeper slope (for the acceleration part). But the graph does not show a clear half - race constant - speed segment.
• Option D: If Runner B had the same acceleration as all three runners, the shape of its graph (in terms of curvature, since acceleration is related to the second - derivative of the distance - time function for constant acceleration, \(s = ut+\frac{1}{2}at^{2}\)) should be similar to the other runners. But Runner B's graph is different from the others.

Answer:

B. Runner B passed Runner C with a burst of speed at the end when Runner C slowed.