GATE CE 2017 Set 2 — Question 36
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Engineering Mathematics → Calculus → Local Maxima & Minima
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Question
Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled (in km) and time (in hour) for both the vehicles are given asP:
Q: Within the first one hour, the maximum space headway would be
Q: Within the first one hour, the maximum space headway would be
Correct answer
(A) 15 km at 30 minutes
Solution
Space headway is the distance between the two cars at any time .
.For the first hour (), , so we can write:
To find the maximum space headway, we differentiate with respect to and set it to zero:
hours.Converting time to minutes:
minutes.Calculating the maximum space headway at :
km.Therefore, the maximum space headway is 15 km at 30 minutes.
.For the first hour (), , so we can write:
To find the maximum space headway, we differentiate with respect to and set it to zero:
hours.Converting time to minutes:
minutes.Calculating the maximum space headway at :
km.Therefore, the maximum space headway is 15 km at 30 minutes.
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