As a safety engineer for FrontRunner, you have given the operators strict instru

Question

As a safety engineer for FrontRunner, you have given the operators strict instructions that they should not exceed 70 mph on a particular section of the track.

One of the operators complained that at times she needed to go a little faster in order to keep on schedule.

You have given strict instructions that this limit of 70 mph is not to be exceeded and safety takes precedence over schedule.

This operator’s train was clocked at 68 mph when passing your safety checkpoint at 1:05 pm.

The train passed another checkpoint 12.5 miles away at precisely 1:14 pm again with a speed of 68 mph

Explain using the Mean Value Theorem how you know that this operator did in fact exceed the safe speed of 70 mph between the two checkpoints.

Explanation / Answer

Limit of 70 mph is not to be exceeded

This operator’s train was clocked at 68 mph when passing your safety checkpoint at 1:05 pm.

The train passed another checkpoint 12.5 miles away at precisely 1:14 pm again with a speed of 68 mph

The time difference between 1:05 and 1:14 is 9 min, which is 9/60 or 0.15 hr

The average velocity V = total distance / time

V(av) = (12.5 miles) / 0.15 hours

V(av) = 83.3333333333333333

So, the average speed in this journey between the two checkpoints is 83.3333. For it to have reached this average speed, it must have crossed the 70 mph mark at some point

So, proved that it did cross 70

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