### 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 ๐ of the object? (A) ๐น is equal to ฮ๐ times ฮ๐ก. (B) ๐น is equal to ฮ๐ก divided by ฮ๐. (C) ๐น is equal to two times ฮ๐ times ฮ๐ก. (D) ๐น is equal to ฮ๐ divided by ฮ๐ก. (E) ๐น is equal to a half times ฮ๐ times ฮ๐ก.

Okay, so in this question, weโre 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 objectโs momentum. In these formulas, the force is denoted as ๐น, the time interval is ฮ๐ก, and the change in momentum is ฮ๐. 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 objectโs 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 weโve been given, the force is denoted as ๐น. The change in momentum of the object is denoted as ฮ๐. And the change in time over which the momentum change occurs is denoted as ฮ๐ก. And so, if we write out this formula in symbols instead of words, that formula becomes ๐น, so thatโs the force, is equal to ฮ๐, thatโs the change in momentum, divided by ฮ๐ก, 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 objectโs momentum is ๐น is equal to ฮ๐ divided by ฮ๐ก.