the value of k and the velocity of the particle when x=-2m?

the acceleration of a particle is defined by the relation a=k(1-e^-x), where k is a constant. knowing that the velocity of the particle is v=9m/s when x=-3m and that the particle comes to rest at the origin, determine

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  • 1 decade ago
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    a = k(1-e^-x)

    Since acceleration is the derivative of velocity, therefore we can write it as

    dV/dt = k(1-e^-x)

    dV = k(1-e^-x)dt

    integral dV = integral [k(1-e^-x)]dt

    V = k ( x - (-x) e^-x)

    V = k x (1 + e^-x)

    when x = -3, v = 9. Put the respective values in above equation.

    9 = k (-3) ( 1 + e^-3)

    k = -3 / (1 + e^-3)

    Solving it, we get

    k = -2.8577223806977896287661130596212

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