8. Mr. McCloskey is driving his truck along a straight road when he notices a sm

Question

8. Mr. McCloskey is driving his truck along a straight road when he notices a small dark object 500 ft ahead. He steps on the brakes, then recognizes that the object is a duck standing in the middle of the road. The truck records his speed every 2 seconds after he applies the brakes until he stops after 10 seconds. time t (sec) 0 2 4 6 8 10 speed (t/sec)100 80 50 25 10 Is it possible that Mr. McCloskey hit the duck? Find lower, midpoint, and upper estimates for the total distance traveled by the truck before coming to a stop. Assume that the speed of the truck decreased throughout the 10-second period but not necessarily at a steady rate

Explanation / Answer

Lower :
We will use the values 80,50,25,10 and 0

Add :
80 + 50 + 25 + 10 + 0, i.e 165

165 * delta(t)

165 * 2

330 ft is the lower estimate

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Upper :
We will use 100,80,50,25,10

Add em up :
100 + 80 + 50 + 25 + 10
i.e 265

265 * delta(t)

265 * 2

530 ft is the upper estimate

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Midpt estimate :
(upper +lower)/2 is a good estimate

(330 + 530)/2

880/2

440 ft

So, no, it is not possible for Mr McCloskey to have hit the duck.

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