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Math Help - Mechanical Exam Question

  1. #1
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    Mechanical Exam Question

    Given that s=ut+at^2 and that the rate of change of distance with time = speed, show that,

    v=u+at


    OK so it is quite simple it's a matter of differentiating the first term. But why exactly?
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  2. #2
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    simply because velocity is defined as the rate of change of position with respect to time.

    specifically ...

    v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}
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  3. #3
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    If you were to differentiate   s(t)=ut+at^2 you would not get  v(t)=u+at you would get  v(t)=u+2at

    Because  s(t)= ut+\frac {1} {2} at^2 given that the object starts at position 0.
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  4. #4
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    my bad, it was a typo.
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