Problem 52654. Easy Sequences 13: Average Speed of Spaceship

Created by Ramon Villamangca

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<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This "back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Given an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> Please round-off your answer to the nearest integer.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">NOTE: Use clasical physics only. Ignore any relativistic effects.</span></span></div></div></div>

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Last Solution submitted on Nov 22, 2022

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ChrisR on 5 Sep 2021

Nice set of problems, Ramon. I particularly like the red herring in this one's test suite.

Ramon Villamangca on 8 Sep 2021

Thanks Chris... :)

Rafael S.T. Vieira on 22 Nov 2022

Tip: This is not a classical-physic-only problem. As far as I know, the digamma function is not taught in high school.

Ramon Villamangca on 19 Dec 2022

By definition classical physics means physics without modern relativity and quantum mechanics.

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Problem 52654. Easy Sequences 13: Average Speed of Spaceship

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Problem 52654. Easy Sequences 13: Average Speed of Spaceship

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