The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 – x3, where x1t2 denotes the p

Question

The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 – x3, where x1t2 denotes the position at time t of the particle. (a) If a particle is located at x = 1 when t = 2, what is its velocity at this time? (b) Show that the acceleration of a particle is

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Diễm Kiều 1 year 2021-09-05T08:05:59+00:00 1 Answers 2 views 0

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    2021-09-05T08:07:07+00:00

    Answer:

    a)V=7 m/s

    b)a=3t²-3x² t³ +3 x ⁵

    Explanation:

    Given that

    [tex]\dfrac{dx}{dt}=t^3-x^3[/tex]

    a)

    We know that velocity V is given as follows

    [tex]V=\dfrac{dx}{dt}[/tex]

    [tex]V=t^3-x^3[/tex]

    At t= 2 s and x= 1 m

    [tex]V=2^3-1^3=7 m/s[/tex]

    V=7 m/s

    b)

    Acceleration a is given as follows

    [tex]a=\dfrac{dV}{dt}[/tex]

    [tex]a=3t^2-3x^2\dfrac{dx}{dt}[/tex]

    Now by putting the values

    [tex]a=3t^2-3x^2\times (t^3-x^3)[/tex]

    a=3t²-3x² t³ +3 x ⁵

    Therefore the acceleration of a particle will be 3t²-3x² t³ +3 x ⁵.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )