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Is my working correct?

  1. Jul 26, 2009 #1
    A car is advertised as taking [tex]11.3\ s[/tex] to reach a speed of [tex]100\ kmh^{-1}[/tex]. About how far does it travel before reaching this speed?

    Firstly I have tried to work out the acceleration: [tex]a=\frac{\frac{100000}{3600}}{11.3}\approx 0.2175\ ms^{-2}[/tex]

    I've then used this to find the displacement: [tex]x=0.2175\times 11.3^2\approx 21.7\ m[/tex]

    Am I doing something wrong? It seems like too short a displacement...

    Thanks for your help
  2. jcsd
  3. Jul 26, 2009 #2
    Check your conversion from [tex]\tfrac{kilometers}{hour}[/tex] to [tex]\tfrac{meters}{second}[/tex].
    Remember that for motion with constant acceleration, starting at rest, [tex]S=\tfrac{1}{2} a t^2[/tex]
    Don't round your results so much. Keep your answer parametric until the very end. This is a skill you'll NEED once you get to the more complicated stuff.
    You were off by a factor VERY different from [tex]10^n[/tex] in your calculation of the average acceleration.

    Another thing I feel I should mention is that you need to state your assumption that the car accelerates with a constant acceleration, as that is not always the case, and your results will vary greatly should you consider such a case.
    Last edited: Jul 26, 2009
  4. Jul 26, 2009 #3
    Awesome. Thanks for your help.
    I'm now getting the answer as [tex]\approx 314\ m[/tex] with
    [tex]a=\frac{2500}{1017}\ ms^{-2}[/tex]
    Is that correct?
    Last edited: Jul 26, 2009
  5. Jul 26, 2009 #4
    That is very close, you forgot the factor of [tex]\tfrac{1}{2}[/tex] in the displacement as a function of time formula.
  6. Jul 26, 2009 #5
    Oh yeah. Oops.

    Thanks again for your help. I'm sure these will become really easy after I do a few more of them.
  7. Jul 26, 2009 #6
    Oh yeah, completely. By the time you get to the subject of work and energy, you'll be reciting these in your sleep. :)

    And no problem, you're very welcome.
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