Another average velocity and speed example

We are told a seal and a penguin are playing a fun game of catch. The penguin swims leftward nine meters, then dodges rightwards another 12 meters. The penguin swims a total time of eight seconds, so goes to the left for 9 meters and then it goes to the right for 12 meters. What is the penguin's average velocity during the chase, and they say answer using a coordinate system where rightward is positive and round answer to two significant digits?

Or really, we should be rounding our answers to two significant digits. So pause this video and see if you can figure out the penguin's average velocity during the chase.

All right, so let's just think about it. Our average velocity, right over here, it is a vector quantity. Sometimes you'll see it written like that, but sometimes when we're thinking about one-dimensional vectors, people don't bother with it. Then, whether we talk about a positive or negative sign, that tells us our direction. But this is going to be equal to our displacement divided by the elapsed time.

Displacement divided by our time. And so what is our displacement? Well, we go 9 to the left, and remember our convention is that the left is negative. So it's going to be negative 9 meters plus 12 meters to the right, 12 meters to the right, all of that over our elapsed time of 8 seconds.

And what's this going to be equal to? Well, negative 9 plus 12 is a net of positive 3 over 8, and our units of course are meters per second. So 3/8 of a meter per second. But they want us to go to 2 significant digits. So I'll write it as a decimal; 3/8 is the same thing as 0.375. But since they want us to round to two significant digits, I'll just say 0.38 meters per second.

That is the penguin's average velocity during the chase. It would be approximately this right over here if we round to two significant digits.

But now, let's think about this next question: What is the penguin's average speed during the chase? Pause this video again and see if you can work through that.

All right, now let's do it together. So our average speed, and we'll use r for rate sometimes, which could be used for speed. Our average speed instead of displacement divided by elapsed time, we're going to be thinking about distance divided by elapsed time.

And with distance, we don't care about the direction; we just care about the magnitude. So we go 9 meters to the left plus 12 meters to the right. One way to think about is the absolute value of each of these values up here. And then we're going to divide that by our elapsed time.

And so this is going to be equal to 21 over 8 meters per second. And let's see, 21 over 8 is equal to 8 goes into 21 2 times; you have 5 left over 2 and 5/8. 5/8 as a decimal is 0.625, so this is going to be equal to 2.625. If they want us to round to two significant digits, it's going to be 2.6. So it's going to be approximately 2.6 meters per second, and we're done.