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Math Help - Dynamics 4

  1. #1
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    Post Dynamics 4

    Hello Everyone, please help me on this dynamics questions!

    A particle moving along a straight line experiences a retardation of 1 + v^2 cm/s^2 when it is travelling at v cm/s. If initially the velocity of the particle is u cm/s, show that it comes to rest instantaneously after Tan^-1 u s. How far has it travelled in this time?
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  2. #2
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    Quote Originally Posted by Modernized View Post
    Hello Everyone, please help me on this dynamics questions!

    A particle moving along a straight line experiences a retardation of 1 + v^2 cm/s^2 when it is travelling at v cm/s. If initially the velocity of the particle is u cm/s, show that it comes to rest instantaneously after Tan^-1 u s. How far has it travelled in this time?
    a = 1 + v^2 \Rightarrow \frac{dv}{dt} = 1 + v^2 \Rightarrow \frac{dt}{dv} = \frac{1}{1 + v^2}.

    Solve for v as a function of t, subject to the condition v = u when t = 0.

    Substitute v = 0 and solve for t.

    Solve \frac{dx}{dt} = v for x as a function of t, subject to the condition x = 0 when t = 0. Substitute the value of t found above and solve for x.
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