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Classical Mechanics Level 2

Two runners have a race. The first runner decides to run with his full speed v 1 = 9 m/s v_1=9~\mbox{m/s} over the 250 meters of the race and then slows to v 2 = 7 m/s v_2=7~\mbox{m/s} for the rest, since he's tired. The second runner wants to save energy, so he runs with v 3 = 8 m/s v_3=8~\mbox{m/s} for the whole time. If the distance of the race is L = 500 m L=500~\mbox{m} , by what time in seconds does the second runner beat the first?

Moral of the story: slightly slower but steadier wins the race.


The answer is 0.992.

David Mattingly by David Mattingly

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1 solution

David Mattingly Staff
May 13, 2014

The time of the first runner is t 1 = 250 / 9 + 250 / 7 = 63.492 s t_1=250/9+250/7=63.492~\mbox{s} . The time of the second runner is 500 / 8 = 62.5 s 500/8=62.5~\mbox{s} . Therefore the second runner beats the first runner by 63.492 − 62.5 = 0.992 s 63.492-62.5=0.992~\mbox{s} .

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