A man begins a car trip to visit his inlaws The total distan

A man begins a car trip to visit his in-laws. The total distance is 60 miles, and he starts off at a speed of 60 miles per hour. After driving exactly 1 mile, he loses some of his enthusiasm for the journey, and (instantaneously) slows down to 59 miles per hour. After traveling another mile, he again slows to 58 miles per hour. This continues, progressively slowing by 1 mile per hour for each mile traveled until the trip is complete. (a). How long does it take the man to reach his in-law? (b). How long would the trip take in the continuous case where the speed smoothly diminishes with the distance yet to travel?

Solution

answer.

a)

Time taken to travel 1st mile = 1/60 hr

time taken to travel 2nd mile = 1/59 hr

time taken to travel nth mile = 1/61-n hr

time taken to travel 60th mile = 1/1 hr

total time = 1/60 + 1/59 + ... + 1/1 hr

Total time taken = 4.67987 ans.

b)for continuous case

The man decreases his speed by 1 mph starting from 60. Hence velocity at any time t would be

v=60-t

where t is in hours.

dxdt=60-t

dx=(60-t)dt

Integrating we get

x=60t-t^2/2+c

We know that he covers a distance of 1 mile with a speed of 60mph. Hence time taken is 1/60h.