As a graduation present Natalie received a sports car which she drives very fast

Question

As a graduation present Natalie received a sports car which she drives very fast but very smoothly. She always covers the 26 miles from her home to the nearest Wal-Mart in less than 30 minutes. To slow her down the local DPS officer, Fred Meaney, decides to change the posted speed limit. Which one of the speed limits below is the highest he can post, but still catch her speeding at some point on her trip? (Hint: Apply the MVT.) Speed Limit = 55 mph Speed Limit = 65 mph Speed Limit = 70 mph Speed Limit = 50 mph Speed Limit = 60 mph

Explanation / Answer

here we have Natalie's average speed. she covers 26 miles in 30 minutes i.e 1/2 hrs. her average speed = 26/1/2 = 52 mph since we know that her average speed is 48.75 mph the mean value theorem tells us that at some point her instantaneous speed must be 48.75mph. She could pull out of her driveway, accelerate to 55mph in seconds and stay there until she slams on the brakes in the parking lot. hence at some point she is going exactly 52mph. so the answer will be 55mph.......option A

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