Video: Calculating the Momentum of an Object from Its Mass and Velocity

A cat has a mass of 3 kg. The cat moves 4 m in a straight line in a time of 2 s. What is the momentum of the cat?

02:42

Video Transcript

A cat has a mass of three kilograms. The cat moves four meters in a straight line in a time of two seconds. What is the momentum of the cat?

Okay, so first of all, here is our cat. And we can draw a diagram showing that it moves four meters in a straight line. Now, since we haven’t been told which direction the cat actually moves in the question, we can simply assume that the cat is moving towards the right. This is an arbitrary choice. But let’s just choose the right for now.

At this point, we can recall that momentum, which we’ll call 𝑝, is defined as the mass of an object multiplied by the velocity of the object. Now, if we’re trying to find the momentum of the cat, then we need to know the mass of the cat and the velocity of the cat. Well, luckily, we already know the mass of the cat. It’s three kilograms. However, we haven’t explicitly been given the velocity of the cat. But, this doesn’t matter because we can recall that the velocity of an object is defined as the displacement of the object, which we’ll call 𝑠, divided by the time taken for the object to be displaced that much.

Now, since we’ve been told that the cat moves four meters in a straight line and we can recall that displacement is the straight line distance between two positions, this means that we know the displacement of the cat because we know that it starts here, as we’ve drawn in the diagram, and finishes up here. The straight line distance between these two positions is four meters. And hence, we know the displacement of the cat.

As well as this, we know the time taken for that displacement to occur. We’ve been told that the cat moves four meters in a time of two seconds. This means that we can work out the velocity of the cat. This ends up being four meters divided by two seconds. And because both displacement and velocity are vector quantities, we need to state their direction. And once again, because we haven’t been given the direction in which the cat moves, we’ve chosen to say that the cat is moving towards the right. Hence, the velocity of the cat is four meters divided by two seconds to the right. Then, when we evaluate this fraction on the right-hand side, we find that the velocity of the cat is two meters per second to the right.

So at this point, we know the mass of the cat and now we know the velocity of the cat. This means we can work out the momentum of the cat. The momentum ends up being the mass of the cat, which is three kilograms, multiplied by the velocity, which is two meters per second to the right. However, at this point, we’re going to stop using this convention to the right because we haven’t actually been told this in the question. We just chose it randomly. So we do not want to give this as a final answer. The only reason we even mentioned the fact that the cat was moving to the right in the first place was because we were dealing with vector quantities. However, realistically, if we haven’t been given the information in the question, then when we give our final answer for the momentum, we should only give its magnitude or size. However, in general, it’s good practice to work with directions as well, especially, if we’ve been given that information.

But, anyway, so the momentum of the cat, or rather the magnitude of the momentum of the cat, is equal to three kilograms multiplied by two meters per second. And so we find that the momentum of the cat is six kilograms meters per second. And this is our final answer to the question.

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