### Video Transcript

A train engine does work at a rate of 5000 watts. How much time will this engine take to do 125 joules of work?

Okay, in this question, we’ve been told that we’ve got a train engine doing work at a rate of 5000 watts. We need to work out how much time the engine takes to do 125 joules of work.

So if we look very carefully, three different quantities have been mentioned in this question. Firstly, there’s work. Secondly, there’s time. And thirdly, there’s a power here because we know that a watt is a unit of measurement of power. So we need to look for a relationship that links together work, time, and power. And, in fact, in this question, we’ve actually been given a hint as to what this relationship is.

We’ve been told that the engine is doing work at a rate of 5000 watts. So the 5000 watts is the power. And we know that the power is the same thing as an engine doing work at some rate. A rate basically means how much of something you do per unit time. So in this case, power is the rate of doing work. Or power is equal to work divided by time.

Now it’s important to be careful here because we’re using 𝑊 to represent work, but we’re also using W here to represent watts. This is a very common problem that occurs. And conventionally, we use 𝑊 to represent both watts and work. So we need to be very, very careful and just make sure that we know which one it is by context.

It should be clear that we’re representing work with 𝑊 when we’re doing the working out. And when we’re putting the numbers with their units, then that will probably represent watts. Well, the point is that is important to know which one we’re working with at any given time.

Now the question asks us how much time will the engine take to do a certain amount of work. So we need to rearrange this equation so we solve for the time. We can do this the following way. We can multiply both sides of the equation by the time divided by the power.

The powers cancel on the left-hand side and the times on the right, leaving us with the time taken is equal to the work done, not watts, work done divided by the power. And now we just substitute in our values. The time taken 𝑡 is equal to the work done, which is 125 joules, divided by the power, which happens to be 5000 watts.

Evaluating this fraction, we find that the time taken to do this amount of work is 0.025 seconds. And the reason we know that the final answer is gonna be in seconds is because we’ve used standard units. So for the work done, we use the standard unit of joules. And for the power, we use the standard unit of watts. Therefore, the time that we find will be in its standard units of seconds. And hence we’ve reached our final answer.