sirenkingofficial,Popular 365 Question

Hey, I'm super stuck on this question.
A time-varying force, F = 24t2 i + (36t-16) j -12 t k N acts on a 2 kg mass. The initial velocity is v0 = 6 i+ 15 j - 8 k m/s. What is the velocity a a time t?
Thanks!

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3 months ago 1

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  1. Steve4Physics

    I'll assume v₀ is the velocity at time t=0 and the impulse acts from t=0 to t=t.

    The total impulse is ∫ F.dt
    = ∫( 24t²i + (36t-16)j - 12tk) dt
    = 8t³i + (18t² - 16t)j - 6t²k

    The initial momentum is mv₀ = 2(6i+ 15j - 8k) = 12i +30j - 16k

    Impulse = change in momentum = final momentum - initial momentum

    You should be able to complete this now.

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