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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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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Answer Clues

## Answers

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.