# Question Video: Understanding the Equation That Links Force- Momentum and Time Physics • 9th Grade

Which of the following formulas correctly relates the force acting on an object, the time for which that force acts, and the change in the momentum 𝑝 of the object? [A] 𝐹 = Δ𝑝Δ𝑡 [B] 𝐹 = Δ𝑡/Δ𝑝 [C] 𝐹 = 2Δ𝑝Δ𝑡 [D] 𝐹 = Δ𝑝/Δ𝑡 [E] 𝐹 = (1/2)Δ𝑝Δ𝑡

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### Video Transcript

Which of the following formulas correctly relates the force acting on an object, the time for which that force acts, and the change in the momentum 𝑝 of the object? (A) 𝐹 is equal to Δ𝑝 times Δ𝑡. (B) 𝐹 is equal to Δ𝑡 divided by Δ𝑝. (C) 𝐹 is equal to two times Δ𝑝 times Δ𝑡. (D) 𝐹 is equal to Δ𝑝 divided by Δ𝑡. (E) 𝐹 is equal to a half times Δ𝑝 times Δ𝑡.

Okay, so in this question, we’re given a bunch of different potential formulas which could relate the force acting on an object, the time that force acts for, and the change in the object’s momentum. In these formulas, the force is denoted as 𝐹, the time interval is Δ𝑡, and the change in momentum is Δ𝑝. We are asked to work out which of the formulas is the correct one.

We can recall that whenever a force acts on an object, it causes the momentum of the object to change. Specifically, the force acting on the object is equal to the rate of change of the object’s momentum over time. Another way of writing this statement is to say that the force is equal to the change in the momentum of the object divided by the change in time over which this momentum change occurs. We have seen that in the formulas that we’ve been given, the force is denoted as 𝐹. The change in momentum of the object is denoted as Δ𝑝. And the change in time over which the momentum change occurs is denoted as Δ𝑡. And so, if we write out this formula in symbols instead of words, that formula becomes 𝐹, so that’s the force, is equal to Δ𝑝, that’s the change in momentum, divided by Δ𝑡, the change in time.

Looking at this formula, we see that it matches the one given in option (D), and so this option must be the correct answer. That is, the formula which correctly relates the force acting on an object, the time for which that force acts, and the change in the object’s momentum is 𝐹 is equal to Δ𝑝 divided by Δ𝑡.

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