Question Video: Identifying the Relationship between Force and Momentum Mathematics

Complete the following: The rate of change in _ with respect to time is equal to the acting force.

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Video Transcript

Complete the following: The rate of change in what with respect to time is equal to the acting force.

Let’s define the acting force to be equal to 𝐹. One of the expressions we have that links force with the rate of change of some quantity is force is equal to d by d𝑡 of 𝑚𝑣. In other words, force is equal to the rate of change of mass times velocity with respect to time. But what do we know about this expression mass times velocity?

Well, we know that momentum is equal to mass times velocity. This means that we can alternatively express force as the derivative of momentum with respect to time. So, the rate of change in momentum with respect to time is equal to the acting force.

And so, the missing word here is momentum.

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