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# Average velocity and speed worked example

## Video transcript

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 pigs average velocity and average speed over this time and assume rightwards is positive and leftwards is negative and round your answer too significant in digit so pause this video and try to work it out on your own alright 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 left words 5 meters so then from there it's going to walk left words 5 meters so 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 it gets right over there so that'd be a displacement of negative 25 meters to eat another nut so it ends up right over it ends up right over there now to figure out our average velocity let me write it down so our velocity average and even though this is one dimensional it is a vector it has direction to it we we specify the direction with the sign positive being right words being positive and left words being negative you oftentimes for 1 dimensional vectors might not see an arrow they 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 a change in X divided by how much time has actually elapsed and so what is our displacement going to be let's see we have plus 20 meters and then we have minus 5 meters and then we go to the left another 25 meters minus 25 meters and then all of that is going to be over the elapsed time or change in time all of that is over 300 seconds so what does this numerator going to be this is 20 minus 30 so that's going to be equal to negative 10 so this is equal to negative 10 meters over 300 seconds over 300 seconds so the average velocity is going to be equal to negative one thirtieth 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 so it's approximately equal to zero point zero three three that would be one thirtieth now let's try to tackle average speed so our speed our sometimes is used for speed R for 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 the whole one of the plates of this problem so our distance divided by elapsed time so what's our distance traveled well it's going to be the absolute value of each of these numbers so it's going to be 20 meters plus 5 meters plus 25 meters notice there's a difference here we're not subtracting the five in 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 50 meters over 300 seconds which is equal to 5 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 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 6 times 6 times 6 is 36 and we're still and then we get let me scroll down a little a little bit more again and then we get another we get another four and then we're just going to keep getting sixes over here so this is going to be approximately equal to zero point one if we want two significant digits one seven meters per second and we are done we figured out the average velocity and the average speed
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