### Video Transcript

If the resultant force acting on a moving body vanishes, it means that its blank vanishes. (A) Displacement, (B) velocity, (C) acceleration, (D) mass.

So we’ve been given this statement here, and our task is to fill in this blank with one of these four possible word choices. We can see that this is a statement about a moving body. So that’s any object with a nonzero velocity. Let’s suppose that this circle here represents our moving object. Since the object is moving, we know that it’s got some nonzero velocity. And let’s suppose for the sake of our sketch that that velocity is directed to the right. This statement is about what happens if the resultant force acting on this object vanishes, that is, if this overall result and force on the object, which we’ve labeled as 𝐹, is zero.

Now, in order to fill in the blank in this statement, we need to recall Newton’s first law of motion. This law says that an object at rest will remain at rest and an object moving with a constant velocity will continue to travel at that velocity unless acted on by an unbalanced force. What this law means is that if there is no unbalanced force acting on an object, or in other words if it has zero resultant force on it, then the object experiences no change in its velocity.

Now in this question, we’re considering a moving body, and we drew that with its velocity pointing to the right. Newton’s first law of motion tells us that if the resultant force acting on this moving body vanishes, then that velocity isn’t going to change. So this object keeps on moving with the same velocity to the right. If we look at answer option (B), this claims that the missing word in the statement is velocity. With this choice, the statement would read, if the resultant force acting on a moving body vanishes, it means that its velocity vanishes. But we know that this can’t be true because the object is moving with some initial nonzero velocity. And we’ve seen from Newton’s first law that its velocity isn’t going to change. That means then that we can eliminate answer option (B).

Let’s now consider answer option (A), which claims that the missing word is displacement. With this choice, the statement says that if the resultant force acting on a moving body vanishes, it means that its displacement vanishes. Let’s recall that the velocity of an object is defined as the rate of change of the displacement of that object with time. Now, we’ve already seen that with zero resultant force acting on it, the object experiences no change in its velocity. So it keeps moving with a constant velocity. That means that the displacement of the object in the direction of this velocity must be continually increasing as time goes on. So we can safely say that the displacement of the object does not vanish if the resultant force acting on it vanishes. And therefore, we can eliminate answer option (A).

Answer option (C) claims that the missing word is acceleration. That is, if the resultant force acting on a moving body vanishes, it means that its acceleration vanishes. Let’s recall that just as an object’s velocity is defined as the rate of change of the object’s displacement with time, the acceleration of the object is defined as the rate of change of the object’s velocity with time. We can also express this mathematically by saying that the acceleration 𝑎 is equal to the change in velocity Δ𝑣 divided by the changing time Δ𝑡 over which that velocity change occurs. We’ve already seen that with zero resultant force acting on it, an object experiences no change in its velocity. That is, in this equation for the acceleration, the value of Δ𝑣 is zero if the resultant force 𝐹 is zero.

If the value of Δ𝑣 is zero, that is, if there is no change in the object’s velocity, then we can see from this equation that the acceleration 𝑎 must also be equal to zero. Of course, this can also be seen from this word definition of acceleration as the rate of change of velocity with time, because if an objects velocity isn’t changing, then the rate of change of its velocity with time must be zero. And so, its acceleration is zero. We can say then that from Newton’s first law of motion, if an object experiences zero resultant force, then its velocity won’t change. And so the object will have zero acceleration.

It’s looking like answer option (C) may well be the correct choice then. To make sure though, we should also check out answer option (D), which claims that the missing word is mass. That is, if the resultant force acting on a moving body vanishes, it means that its mass vanishes. We can notice that Newton’s first law of motion doesn’t say anything about the mass of the object. And that’s because whether or not there’s a resultant force acting on an object, it can’t change the object’s mass. This object will have some value of the property mass, which we can label as 𝑚. Common sense tells us that this mass can’t just disappear if the resultant force acting on the object vanishes. That means we can safely eliminate answer option (D).

We are left then with the answer given in option (C). The missing word is acceleration. If the resultant force acting on a moving body vanishes, it means that its acceleration vanishes.