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Cheetah problem in watts

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data

    The cheetah is one of the fastest-accelerating animals, because it can go from rest to 3.4 m/s (about 8 mi/h) in 0.5 s. If its mass is 112 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in watts and horsepower.


    2. Relevant equations



    3. The attempt at a solution

    v = u + at ...since the cheetah is initially at rest , u = 0 m/s therefore
    v = at and we have a = (v/t)

    Now power is defined as rate of doing work

    P = ( Force x displacement ) / time
    P = (ma x s) / t where s is the displacement s = vt
    P = (m) * (v/t) (vt) divided by time t

    finally doing all the algebra gives us

    P = mv ^2/ t
    P = (112 x 3.4^2) / 0.5
    P = 2589.4

    are my units wrong? but where?
     
  2. jcsd
  3. Oct 13, 2009 #2

    rl.bhat

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    Displacement s = average velocity* time.
    So s = vt/2
     
  4. Oct 13, 2009 #3

    mgb_phys

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    Or you could simply find the change in KE and power = change in ke/time
     
  5. Oct 13, 2009 #4
    so would it be p= {m(v/t)(vt/2)}/t
    p= 1294.7 watts

    is that right?
     
  6. Oct 13, 2009 #5

    rl.bhat

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    No. It is only m*v^2.
    Power = 1/2*m*v^2/t
     
  7. Oct 13, 2009 #6
    ok so 1/2*m*v^2/t
    =1/2*112*3.4^2/0.5
    =1294.7

    is that it?
     
  8. Oct 13, 2009 #7

    rl.bhat

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    Oh! Sorry. You are right.
     
  9. Oct 13, 2009 #8
    yup thanks so much :)
     
  10. Oct 13, 2009 #9

    DaveC426913

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    Gold Member

    Really? I'm pretty sure if I started with a big leap, I could hit 8mph in not much more than .5s. Is that a high acceleration?

    "...a cheetah can go from 0 to 60 miles (96 kilometers) an hour in only three seconds..."
    http://animals.nationalgeographic.com/animals/mammals/cheetah.html

    So, 0 to 8 in the first .5s, then 8 to 60 in 2.5s.

    OK, that's nearly the same slope... (8/.5 = 16) versus (52/2.5 = 20.8).
     
    Last edited by a moderator: Apr 24, 2017
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