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Constant velocity Problem

  1. Nov 4, 2008 #1
    1. The problem statement, all variables and given/known data

    Speedy tortoise can run 10cm/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2 minutes. The tortoise wins the race by a shell (20cm). A)How long does the race take? B)What is the length of the race.

    2. Relevant equations

    3. The attempt at a solution
    For some reason I am lost on how to set up this problem. I keep wanting to use motion in 1 dimension with constant acceleration but I cannot come up with the answers given in the book. A step by step explanationj on how to solve this type of question would be awesome.

  2. jcsd
  3. Nov 4, 2008 #2


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    This question is probably a little simpler than you're trying to make it.

    Okay, let's start by writing down what we know. Suppose that the length of the track is L and the time taken for the tortoise to complete that race, T, such that

    [tex]v = \frac{dx}{dt}\Rightarrow 10 = \frac{L}{T}[/tex]

    Next we have the hare's information. We know that the hare stops of 2 minutes or 120 seconds, so the total time the hare is running is T-120. We also know that when the tortoise is at the finish line (x=L), the hare is 20cm behind him, i.e. x=L-20. Finally, we know that the hare can run at 20x10 cm/s. Hence,

    [tex]v = \frac{dx}{dt}\Rightarrow 200 = \frac{L-20}{T-120}[/tex]

    Do you follow?
  4. Nov 4, 2008 #3
    Ok I think I follow you. When I was trying to come up with my equations I was taking the hare's distance to be equal to the tortoise's distance minus 20cm. SO should I take those equations and solve one for (T)ime and then put that equation into the other one?
  5. Nov 5, 2008 #4


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    That's exactly what I've done with my set of equations, L-20
    Sounds good to me :approve:
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