Average velocity and speed worked example | One-dimensional motion | AP Physics 1 | Khan Academy

We are told a pig runs rightward 20 meters to eat a juicy apple. It then walks leftward 5 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? 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. 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 can say that's a positive 20 meter displacement. It goes plus 20 meters and ends up right over there. Then it walks leftwards 5 meters, so then from there it's going to walk leftwards 5 meters. We could call that a negative 5 meter displacement.

And then finally, it walks leftward another 25 meters. So then it walks leftward another 25 meters, ending up right over there. 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. Our average velocity is, and even though this is one-dimensional, it is a vector. It has direction to it. We specify the direction with the sign; positive being rightward and negative being leftward. Oftentimes, for one-dimensional vectors, you 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 change in x divided by how much time has actually elapsed.

So what is our displacement going to be? Let's see. We have plus 20 meters, and then we have minus 5 meters. Then we go to the left another 25 meters, minus 25 meters, and all of that is going to be over the elapsed time 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 going to be equal to negative 10. 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 want to specify this as a decimal with two significant digits, this is going to be approximately equal to 0.033, that would be 1/30.

Now let's try to tackle average speed. So our speed, sometimes referred to as speed or rate, our average speed is not going to be our displacement divided by our elapsed 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 elapsed time—what's our distance traveled? What's going to be the absolute value of each of these numbers? It's going to be 20 meters plus 5 meters plus 25 meters. Notice there's a difference here. We're not subtracting the 5 and the 25; we're just adding all of that. We just care about the magnitudes divided by 300 seconds.

So this is going to be equal to 50 meters over 300 seconds, which is equal to 5/30, which is equal to 1/6 of a meter per second.

And if we want to write it as a decimal, let's see. 6 goes into 1. Let's put some zeros here. 6 goes into 10 one time. 1 times 6 is 6. I could scroll down a little bit, and then we subtract; we get a 4. 6 goes into 40 six times. 6 times 6 is 36.

And then we still get—let me scroll down again a little bit more—again, we get another 4, and then we're just going to keep getting sixes over here. So this is going to be approximately equal to 0.17 meters per second if we want two significant digits.

And we are done. We figured out the average velocity and the average speed.