Given an acceleration vector, initial velocity u0,v0,w0 , and initial position x0,y0,z0 , find the velocity and position vectors for t ge 0.

Question

Given an acceleration vector, initial velocity u0,v0,w0 , and initial position x0,y0,z0 , find the velocity and position vectors for t ge 0. a(t) = 5,5t,8t , u0,v0,w0 = 15,0,0 , x0,y0,z0 = 0,0,0 What is the velocity vector?

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Amaya 2 weeks 2021-11-21T14:31:07+00:00 1 Answer 0 views 0

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    2021-11-21T14:32:55+00:00

    Answer:

    Thus we find that velocity vector at time t is

    (5t+15, 5t^2/2, 4t^2)

    Step-by-step explanation:

    given that acceleration vector is a funciton of time and at time t

    a(t) = (5,5t, 8t)

    v(t) can be obtained by integrating a(t)

    v(t) = (5t, 5t^2/2, 4t^2)+(u_0,v_0,w_0)\\=(5t+15, 5t^2/2, 4t^2)

    Thus we use the fact that acceleration is derivative of velocity and velocity is antiderivative of acceleration.

    The arbitary constant normally used for integration C is here C vector = initial velocity (u0,v0,w0)

    Position vector can be obtained by integrating v(t)

    Thus we find that velocity vector at time t is

    (5t+15, 5t^2/2, 4t^2)

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45:7+7-4:2-5:5*4+35:2 =? ( )