A spaceship ferrying workers to Moon Base I takes a straight-line path from the

Question

A spaceship ferrying workers to Moon Base I takes a straight-line path from the earth to the moon, a distance of 384000 km. Suppose it accelerates at an acceleration 19.5 m/s^2 for the first time interval 14.2 of the trip, then travels at constant speed until the last time interval 14.2 min , when it accelerates at 19.5 m/s^2 , just coming to rest as it reaches the moon.

1)What is the maximum speed attained? km/s
2)What fraction of the total distance is traveled at constant speed?
3)What total time is required for the trip? (s)

Explanation / Answer

Let the time traveled with maximum velocity = t (a) maximum velocity = at = 19.5*14.2*60 = 16,614 m/s = 16.614 km/s (b)total distance = 384000 km 384000 = (16.614+0)/2 * 14.2*60 + t*16.614 + (0+16.614)/2 * 14.2*60 t = 22261 seconds = 371 min distance traveled with max speed = 371*60*16.614 = 369845 km fraction = 369845/384000 = 0.963 (c)total time = 14.2+371+14.2 = 399.4 min

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