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1D-kinematics with constant acceleration

  1. Feb 15, 2015 #1
    1. A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time the figure.............. http://postimg.org/image/4q40kyrnx/ [Broken]

    What distance does the cat move from t=0 to t=7.5s?



    2. Relevant equations
    a=dv(t)/dt
    x(t)=x0 +∫v(t)dx

    3. The attempt at a solution
    From the graph I got v(t)=(-4/3)*t + 8

    I integrated and got x(t)=(-4/6)*t^2 + 8*t
    I evaluated at the the upper and lower limits and got 22.5 cm for the answer but got it wrong
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 15, 2015 #2
    Just add the area under the line.
     
  4. Feb 15, 2015 #3

    TSny

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    Hello, and welcome to PF!

    Your work looks good for finding x(t). You are asked for the distance traveled. Is that the same thing as the displacement?
     
  5. Feb 15, 2015 #4
    I thought that was how you're supposed to solve for distance traveled. I don't really know what else to do.
     
  6. Feb 15, 2015 #5

    TSny

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    Does the cat ever turn around and walk back in the opposite direction? Did you take that into account?
     
  7. Feb 15, 2015 #6
    So then at -4/3*t + 8=0 the cat reaches its maximum displacement of 24 cm @ t=6s. and at t=7.5s the cat is at 22.5 cm, so the distance is equal to 24cm + 1.5cm= 25.5cm?
     
  8. Feb 15, 2015 #7

    TSny

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    Yes, at least that's what I would interpret as distance traveled.
     
  9. Feb 15, 2015 #8
    Yes you are right, thank you friend!
     
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