Force as the Time Derivative of Momentum

Question

The momentum of a system is described by the function $$p(t) = A \sin(\omega t) + Bt$$, where $$A$$, $$B$$, and $$\omega$$ are constants. At what times $$t$$ is the net external force on the system zero?

Accepted Answer

When $$t = \frac{1}{\omega} \cos^{-1}\left(-\frac{B}{A\omega}\right) + \frac{2\pi n}{\omega}$$ and $$t = -\frac{1}{\omega} \cos^{-1}\left(-\frac{B}{A\omega}\right) + \frac{2\pi n}{\omega}$$, where $$n$$ is any integer

Answer

Never; the force is always non-zero

Answer

When $$t = \frac{(2n+1)\pi}{2\omega}$$, where $$n$$ is an integer

Answer

When $$t = \frac{B}{A\omega}$$

Force as the Time Derivative of Momentum

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