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Easy problem but i'm getting something wrong please help

  1. Feb 23, 2004 #1
    In a grocery store, you push a 14.5 kg shopping cart with a force of 11.0 N. If the cart starts at rest, how far does it move in 3.00 s?

    i've got that acceleration = force/mass

    so the acceleration i got was .7586
    but for some reason i keep getting the answer to the problem wrong

    theanswer is in meters

    _____m
     
  2. jcsd
  3. Feb 23, 2004 #2

    Integral

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    How are you finding the distance?

    Please show us what you have done.
     
  4. Feb 23, 2004 #3
    Think I'll just let Integral handle it...

    Just ignore this post.

    cookiemonster
     
  5. Feb 23, 2004 #4
    my work

    as i got .7586 m/s2 as the acceleration,

    i multiplied by 3 seconds to get 2.28 m/s

    then i multiplied 2.28x 3 seconds to get 6.83 meters
     
  6. Feb 24, 2004 #5

    ShawnD

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    But it wasn't going 2.28m/s the whole time. That's the problem.

    You know the velocity formula obviously. Just integrate that to get a distance formula.

    [tex]d = \int V dt[/tex]

    [tex]d = \int (V_i + at) dt[/tex]

    [tex]d = V_it + \frac{1}{2}at^2 + d_o[/tex]

    Sorry for making it sound complicated, I just wanted to write that

    The answer should be 3.4137m
     
    Last edited: Feb 24, 2004
  7. Feb 24, 2004 #6

    HallsofIvy

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    Re: my work

    ShawnD pointed out your error: the final speed, at the end of the 3 seconds is 2.28 m/s. It was not going at that speed all the time. If you have not taken calculus, you can use this "short cut": as long as the acceleration is a constant, you can find the "average" speed by averaging the first and last speeds.

    The shopping carts initial speed was, of course, 0. After 3 seconds, it had a speed of 2.28 m/s. The average speed was (2.28+0)/2= 1.14 m/s. How far did the shopping cart go at an average speed of 1.14 m/s for 3 seconds?
     
  8. Feb 24, 2004 #7

    ShawnD

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    Oh cool. I didn't know you could do that.
     
  9. Feb 24, 2004 #8

    Integral

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    One of the given equations in a non calculus class is something like

    [tex] x= \frac 1 2 a t^2 + v_0t + x_0 [/tex]

    For this problem

    [tex] v_0 =0 [/tex] and [tex] x_0 = 0 [/tex]

    you have a and t, simply do the computation to get the same result obtained above.
     
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