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## High school physics

### Unit 1: Lesson 3

Average velocity and average speed

# Average velocity and speed worked example

Sal solves a word problem to find average velocity and speed of an object in one-dimension.

## Video transcript

- [Instructor] We are told a pig runs rightward 20 meters to eat a juicy apple. It then walks leftward five meters to eat a nut. Finally it walks leftward another 25 meters to eat another nut. The total time taken by the pig was 300 seconds. What was the pig's average velocity and average speed over this time? And assume rightwards is positive and leftwards is negative and round your answer to two significant digits. So, pause this video and try to work it out on your own. All right, now let's do this together and first let's just draw a diagram of what is going on. So, this is our pig. It first runs rightward 20 meters, so we could say that's a positive 20-meter displacement, so it goes plus 20 meters, ends up right over there. Then it walks leftwards five meters, so then from there it's gonna walk leftwards five meters, so we could call that a negative five-meter displacement and then finally, it walks leftward another 25 meters. So, then it walks leftward another 25 meters, so it gets right over there, so that would be a displacement of negative 25 meters to eat another nut, so it ends up right over there. Now, to figure out our average velocity, let me write it down, so our velocity average and even this is one dimensional, it is a vector, it has direction to it. We specify the direction with the sign positive being rightwards being positive and leftwards being negative. You oftentimes for one-dimensional vectors might not see an arrow there or might not see it bolded and just written like this. But our average velocity is going to be equal to, you could view it as our displacement or our change in X divided by how much time has actually lapsed and so, what is our displacement going to be? What's it? We have plus 20 meters and then we have minus five meters and then we go to the left another 25 meters, minus 25 meters and then all of that is going to over the elapsed change or change in time, all of that is over 300 seconds. So, what is this numerator going to be? This is 20 minus 30, so that's gonna be equal to negative 10, so this is equal to negative 10 meters over 300 seconds. So, the average velocity is going to be equal to negative 1/30 meters per second, the negative specifies that on average the velocity is towards the left. If you wanna specify this as a decimal with two significant digits, this is going to be, so this will approximately equal to 0.033. That would be 1/30. Now let's try to tackle average speed. So, our speed, R sometimes is used for speed, R for rate, our average speed is not going to be our displacement divided by our lapsed time, it is going to be our distance divided by our elapsed time and we'll see that these are not going to be the same thing. That's one of the points of this problem, so our distance divided by our lapsed time. So, what's our distance traveled? Well, it's gonna be the absolute value of each of these numbers, so it's gonna be 20 meters plus five meters plus 25 meters. Notice, there's a difference here. We're not subtracting the five and the 25, we're just adding all of that. We just care about the magnitudes. Divided by 300 seconds and so, this is going to be equal to 50 meters, over 300 seconds which is equal to five over 30 which is equal to 1/6 of a meter per second and if we want to write it as a decimal, let's see, six goes into one, let's put some zeros here, six goes into 10 one time, one times six is six, I can scroll down a little bit and then we subtract, we get a four, six goes into 40 six times, six times six is 36 and then we get, let me just scroll down a little bit more again and then we get another four and then we're just gonna keep getting sixes over here, so this is gonna be approximately equal to 0.1, if we want two significant digits, 17 meters per second and we are done. We figured out the average velocity and the average speed.