6 points SCalcET8 6.1.053 Two cars, A and B, start side by side and accelerate f

Question

6 points SCalcET8 6.1.053 Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their velocity functions and a 2. 2a t (min) (a) Which car is ahead after two minutes? car A ·car B Explain. The area under curve A is greater than the area under curve B. 0 The area under curve B is greater than the area under curve A. (b) What is the meaning of the area of the shaded region? O It is how much faster A is traveling than B after 2 minutes O It is how much faster B is traveling than A after 2 minutes. O It is the distance by which A is ahead of B after 2 minutes O It is the distance by which B is ahead of A after 2 minutes. (c) Which car is ahead after four minutes? car A O car B Explain. 0 The area under curve A is greater than the area under curve B O The area under curve B is greater than the area under curve A (d) Estimate the time t at which the cars are again side by side. min Show My Workont 7 O Type here to search

Explanation / Answer

Q(a) and (b)
Car A has the higher velocity for the entire first two minutes, so it will have covered more distance. Because distance is the integral of velocity functions, the distance can be interpreted as the area under the curves. Because car A has more area under the curve, it is farther ahead (more distance).

Q(c) and (d) are more judgment calls. After four minutes, you need to decide if car A or car B has more area under its curve.Personally, I think they are about equal. So at four minutes,neither car would be ahead, but instead be side by side.

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