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 . Suppose it accelerates at an acceleration 19.5 for the first time interval 14.2 of the trip, then travels at constant speed until the last time interval 14.2 , when it accelerates at 19.5 , just coming to rest as it reaches the moon.

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

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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