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25 June, 07:17

A force with magnitude 20 N acts directly upward from the xy-plane on an object with mass 4 kg. The object starts at the origin with initial velocity vs0d - i 2 j. Find its position function and its speed at time t.

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  1. 25 June, 08:54
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    Answer:position function at time, t=r (t) = ti-tj+5t^2K+C

    Speed at time, t=square root (2+25t^2)

    Step-by-step explanation: Force = mass * acceleration = F=ma

    a=f/m

    Given: force=20N, Mass=4kg

    a=20/4=5m/s

    a (t) = 5K. Using integration

    V (t) = 5tK+C

    Where C is constant of integration.

    Given:v (0) = i-j

    V (0) = 5 (0) + K

    Zi-j=0+C integrating to get the position function gives:

    r (t) = ti-tj+5t^2 K + C

    C=0 because object started at origin

    Speed is magnitude of velocity

    V (t) = i-j+5t K

    /v (t) / : squareroot (1^2 + (-1) ^2) + 5t^2

    Speed = squareroot (2+25t^2)
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