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.
