Video Transcript
With what constant velocity does an object of mass five kilograms move if its momentum is 10 kilograms meters per second?
Okay, so we have some object. Let’s represent that object by this point here. And the question tells us that this object has a mass which we’ll call 𝑚, which is equal to five kilograms. We’re also told that this object has a momentum, which we’ll call 𝑃, and 𝑃 is equal to 10 kilograms meters per second. Remember that momentum is a vector quantity, which means that it should have a direction as well as a numerical value. For this question, we aren’t told in which direction the momentum is in. So, for the sake of drawing a diagram, let’s assume it’s to the right.
Given all this information, the mass of the object and its momentum, we are asked to find the velocity 𝑣 of the object. Remember, the velocity is also a vector quantity. So, it has a direction as well as a numerical value. And since we’ve assumed the momentum is to the right, the velocity of the object will also be to the right. But since the question doesn’t specify the direction of the momentum or the velocity that we should calculate, we’ll just talk about the numerical value of these two things, and we won’t give their direction each time we write them down.
So, how we’re going to calculate the velocity of this object? Let’s start by writing down the general equation for the momentum of an object, which is that momentum 𝑃 is equal to the mass of the object 𝑚 times its velocity 𝑣. For this question, we’re told the mass of the object and we’re also told the momentum of the object. So, we can use this equation to solve for the velocity 𝑣. We’re told that the momentum of the object 𝑃 is equal to 10 kilograms meters per second.
So, from our equation for momentum, we know that 𝑃 will be equal to the mass of the object, which is five kilograms, times the velocity of the object, which we’re calling 𝑣 and is our unknown variable in this situation. So, now, we need to solve this equation for 𝑣. We can do this by dividing by five kilograms.
If we first look at the units on the left-hand side of this equation, we see that the kilograms in the top and bottom cancel out, and we’re just left with meters per second. And if we then look at the numerical part of the left-hand side, we just have 10 divided by five, which is equal to two. And on the right-hand side of this equation, the only thing we’re left with is 𝑣, our velocity that we’re trying to find. This means that we have our final answer, and the velocity 𝑣 of the object is equal to two meters per second.
