Interesting Usain Bolt problem

Classical Mechanics Level pending

Usain Bolt is the world recorder in 200 m 200\text{ m} run with the time 19.3 s 19.3\text{ s} . Lets assume that Bolt during the record breaking had the following:

  1. he was accelerating constantly first 3.6 s 3.6\text{ s} .
  2. next 100 m 100\text{ m} he was travelling with a constant speed.
  3. last part of the race he was constantly slowing down.
    You also know that he passes the first 100 m 100\text{ m} for a time of 10 s 10\text{ s} .
    . What was the Usain's speed when he ran through the goal? Give your answer up to 2 decimal points.


The answer is 8.61.

Dragan Marković by Dragan Marković , 26, Serbia

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1 solution

Dragan Marković
Apr 25, 2016

Lets denote:
t=19.3s s=200m t'=3.6s s'=s''=100m t''=10s v=?
we know that s''= a t ′ ∗ t ′ 2 \frac{at'*t'}{2} +v' (t''-t')
also v'=at'
with a little rearranging we get that a=3.39 m s ∗ s \frac{m}{s*s}
next s1= a t ′ ∗ t ′ 2 \frac{at'*t'}{2} =21.97m
s2=s-s1-s'=78.03m
s2=v't3- a ′ t 3 ∗ t 3 2 \frac{a't3*t3}{2}
where t3=t-t'-t2
where t2=s'/(a
t')
after calculating we get that a'=0.479 m/s s
in the end v v=v'*v'-2a's2 and v=8.61m/s

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