Question Video: Calculating the Momentum of an Object from Its Mass and Velocity Physics • 9th Grade

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?

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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 in this question, we’ve been told that we’ve got a cat which has a mass, which we will call 𝑚, of three kilograms. We’ve also been told that the cat moves four meters in a straight line in a time of two seconds. So, let’s say that the cat starts here and ends up here. And we can say that the distance moved by the cat is four meters, and it does this in a time of two seconds. Based on this information, we’ve been asked to find the momentum, which we will call 𝑝, of the cat. So, let’s first start by recalling that the momentum of an object 𝑝 is defined as the mass of that object multiplied by its velocity. So, if we want to find the momentum 𝑝 of our cat, we need to know its mass and its velocity. Well, we already know its mass. We know that it’s three kilograms.

However, we haven’t been given its velocity in this question. What we’ve been given, instead, is enough information to calculate this cat’s velocity. Let’s recall that the velocity of an object is defined as the displacement 𝑠 of the object divided by the time taken for the object to travel that displacement. Now, the displacement 𝑠 of an object is simply the distance between its start point and its finish point in a straight line. And luckily, we’ve been told that the cat moves in a straight line. Therefore, in this particular case, the cat’s displacement is four meters. And the time taken to move that displacement 𝑡 is two seconds. Hence, we can say, first of all, that the velocity of our cat is equal to the displacement, which is four meters, divided by the time taken to travel that displacement, which is two seconds. And this gives us a numerical value of four divided by two and a unit of meters divided by seconds or meters per second.

And so, we find that the velocity of our cat is two meters per second. And because velocity is a vector quantity — which, in other words, means that it has magnitude and direction — we can say that the velocity is in the same direction as the cat’s displacement, which is also a vector quantity. In this case, we’ve drawn it as moving toward the right. However, we haven’t actually been given this information in the question. We just sort of assumed that the cat was moving toward the right when we drew our diagram. So here, we don’t need to worry too much about the direction in which the cat is moving. And therefore, we don’t need to worry about the direction of the cat’s velocity. All we care about is that the cat’s velocity has a magnitude of two meters per second.

This means that we can now calculate the cat’s momentum 𝑝, which happens to be the mass of the cat — which we know is three kilograms from the question — multiplied by its velocity — which we’ve just calculated to be two meters per second in the line above. And so, we find that the momentum 𝑝 of the cat has a numerical value of three times two, which is six, and a unit of kilogram times meters per second, which is kilogram meters per second. Hence, our answer is that the cat has a momentum of six kilogram meters per second. And once again, even though momentum is a vector quantity — that is, it has magnitude and direction — because we haven’t explicitly been told the direction in which the cat is actually moving, we don’t need to give the direction in our answer. We can simply say that our cat has a momentum of six kilogram meters per second.

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