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Is it possible to integrate .|' v^2dx ?

Integrate velocity squared over distance? I do not have an expression for velocity or acceleration. Can you help me integrate this?

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  • 8 years ago
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    You say you do not have an expression for acceleration or velocity, but do you have one for position? If you do this is quite a simple integral. Velocity is the first derivative of the position function so v^2 would just be that derivative squared.

    example:

    s(x) = x^2 +4x + 2 <------------ position function

    v(x) = 2x + 4 <-------------- velocity function

    v^2 = (2x + 4)^2

    ∫(2x + 4)^2 dx

    u = 2x + 4

    du = 2 dx

    dx = 1/2 du

    ∫ u/2 du

    u^2/4 + C

    (2x + 4)^2/4 + c

  • 8 years ago

    well velocity itself is distance per unit time like meters/second. The velocity is the derivative of a position function. Acceleration is the derivative of velocity.

    in this case v^2 is treated as a constant because the differential is dx. so the integral would be (v^2)x+c, where c is a constant. You add c to indefinite integrals.

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