Consider the graph below, which shows how the positions of two bicycles (called

Question

Consider the graph below, which shows how the positions of two bicycles (called A and B) change as time passes. The units of position are miles; the units of time are hours. (a) According to the graph, during the last half-hour of the bike ride, when is bike A moving the fastest? t= (b) At about what time does bike B start catching up with bike A? That is, when does the distance between bikes A and B start to shrink? t (c) There is a time when bikes A and B are moving at exactly the same velocity. Estimate that time by looking at the graph. t

Explanation / Answer

a) Bike A is fastest when the slope for its velocity is the steepest in the interval t=1/2 and t= 1. Which is at t = 1/2.

b) Somewhere around t = 3/8. You can not that both the curves have straightened out a bit after that. (Its hard to pin point the exact time without the equation).

c) Yes. You can visualize a time where the tangents to both curves (the velocities) will be parallel to each other. This is when the velocities will be equal. (Again, it is hard to pin-point the exact time if curve equation is unknown).

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