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Math Help - Another Motion Quesiton

  1. #1
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    Another Motion Quesiton

    Margaret has found that by a proper choice of gears she can steadily increase her speed on her bike. One day she sets out and, ten minutes later, she achieves her cruising speed of 30 km/h by increasing steadily. How far did she travel in this time?


    No idea where to begin
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  2. #2
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    I suggest you use the equation of motion.

     V = Vi + at
    30km/h = 8.333m/s
     8.333m/s = 0 + a(10*60)
    a = 0.014m/s^{2}

    Use the other equation of motion

    d =\frac{1}{2}at^{2}
    d = \frac{1}{2}(0.014)(600)^{2}= 2500meters = 2.5 km
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  3. #3
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    If your acceleration is constant, just use rise/run from (0,0) to (10,30) to calculate it. Then you can just use a distance equation for your first integral of 3/2x^2. Not really a calc question.
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  4. #4
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    Yeah we're not using distance equations like that though
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  5. #5
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    Then follow the other suggest.

    Use the fact that

    Vi= 0
    Vf = 30km/h

     a =\frac{dv}{dt}

    Then integrate the acceleration equation twice with respect to time to find the distance.
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  6. #6
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    Alright sorry thank you both
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