Scalars and Vectors example

Transcript

in the previous video we compared vectors and scalers and so now let's look at an example to help us understand so Mr Richardson rode his bike to school rode West at 20 km per hour for 10 minutes then he stopped for 5 minutes to take a rest then he took 15 minutes to Ride 3 km North okay it might be helpful if we draw a picture of what's Happening Here so you Rod West let's do it down here Road West for 10 minutes it's a good idea to draw a little picture sometimes with these word problems helps you break it down into its parts so there's 10 minutes for West oh and then a five minute rest because she's kind of out of shape and then 15 minutes to Ride 3 kilm North okay so 15 minutes and 3 km North okay and this is the start we'll call this the origin origin means start okay we don't know how far he traveled here at first we know he traveled for 10 minutes and he traveled at 20 km per hour 20 km per hour and 1 hour is 60 minutes so that's the same thing and that lets the minutes cancel and if you put that in your calculator you should get 3.3 km so this is 3.3 km okay if that is confusing for you please go and see the video called unit conversions so the distance travel is pretty simple the first part was 3.3 km and then he went 3 km North so the total distance is 6.3 km now let's look at the displacement now remember displacement is the change in position so we start started here at the origin finished here so his displacement is this distance here so here we have a right triangle we're going to use some Pythagorean theorem to calculate this his displacement so we got 3.3 2 + 3^ S gives us d^2 displacement squar the displacement squared okay now I'm going to assume that you know how to do Pythagorean theorem and I'm going to skip to the answer here which is displacement is equal to 4.5 km Northwest remember it has to be a Direction and it's Northwest because it's up and to the left now if you don't understand how I got this uh you can come and see me and we can go through it average speed that's the we can write it like this that's the speed that's the average speed is the total distance over the total time so that was 6.3 kilm it's the total distance over the total time total time of the trip was 30 minutes 15 plus 5 + 10 is 30 minutes and that works out to. 21 kilm per minute now kilomet per minute that's okay that's not wrong but usually we don't use kilometers per minute usually it's kilometers per hour or meters per second it doesn't really matter but let's just change this into kilometers per hour just so you can C 21 km per minute that's the same as writing it this way multiply by a conversion factor which is 60 Minutes is the same as 1 hour minutes cancels and we get 12.6 k hour notice there's no Direction because this is speed and speed is a scaler now you might be looking at this and you might be thinking yeah I get this this is easy please use your calculator and check it for yourself pause the video and check it for yourself the last thing to do is look at average velocity our average velocity is the like that and it's the displacement over time and we've established that the displacement was 4.5 km Northwest the time is still 30 minutes and that gives us 0.15 kilm per minute Northwest or if you convert it to kilometers per hour you should get 9 kilomet per hour Northwest