Answers for the SteemYourBrain Challenge #1 !
The Epic(?) SteemYourBrain Challenge #1 has ended :)
Thanks everyone for participating and supporting such contest!
Link the the Question post: https://steemit.com/math/@happychau123/steemyourbrain-challenge-1-2-3-sbd-reward-2017629t5175327z
First, we write down an equation to describe the question:
500m/t1 = v1
500m/t2 = v2
1000/(t1+t2) = 2v1
By simple substitution, we get:
2v1t1+2v2t2 = 1000
v2t2 = 0
t2 = 0/v2
, in which you need infinite fast speed to finish the last 500m
, which is, mathematically possible. (2SBD)
How about physically?
By the famous relativity, we all know that speed limit of anything is 300000000m/s,
But!! That doesn't make the run impossible.
Let's take the frame of reference to be the track, When you are running at c, the speed is calculated as c/t hence 300000000m/s, but not infinitely.
How about we take the frame of reference to be on the runner, things gets more interesting now.
Now the runner is at stationary, the track is moving towards him at c,
under this situation, the length of the track becomes 0, hence the runner can finish it in zero second.
But!, due to length contraction, the runner actually only moved 500m in tv1, so the average speed is still, v1.
It is an impossible action to be performed physically :) (3SBD)
The 2SBD trivial solution prize goes to 
The 3SBD tricky solution prize goes to the only one mentioning relativity with explanations for possibility
More and more of tricky questions are coming!
See you next time !:D