Now I really love this question it’s very ap style with a couple of unique things says the study suggests between the hours of 1:00 and 4:00 on a normal weekday the speed of the traffic is given by this formula alright and speed is measured in kilometres per hour not miles per hour in your units matter and T is.
Measured in the hours past noon it’s not the hours past midnight and that matters okay we are going to be able to use our calculator on this but it wants us to compute the.
Average speed of the traffic between the hours of 1:00 and 4:00 all right so there’s a lot of information in there it asks for average speed this function represents speed if that is the case then the average speed is going to be the average value so the average speed is going to be.
I’m going hours past noon remember so the hours past noon okay one is can just be 1 and 4/10 just be for.
Now if it was measured in hours after midnight then.
One would be a 13 right and 4 would be a 16 so it really does matter when the time you know. or something like that so you’ve got to be careful what you’re given this is going to be.
4 minus 1 and then we’re going to integrate from 1 to 4 and we’re going to integrate s of T please don’t put f of X we’re going to integrate s of T DT now it did say that we could use our calculator so let’s go ahead and use math 9 all right so if we use math.
Going to end up 1/3 times we’re going to get 1 96.
5 now if you tried that in your calculator and that’s what you got great I recommend you try it because if you aren’t putting stuff in the calculator right obviously it’s going to hurt you so this is going.5 do not put miles per hour that is in kilometers per hour okay that is going to be the average speed from 1 to 4 now I like talking about this because we’re if we’re going to break down the unit’s here all right remember I was given speed so if.
Average speed therefore the average speed requires average value we cannot use the F of B minus F of a over B minus a kind of formula alright now let’s talk a little bit about our unit so why does this work okay we’re a unit breakdown is actually kind of interesting remember all.
Of our even related rates and all those things that we’ve done okay all the units do match up sometimes we just kind of skip over them but the units do match so here’s what we’re.
Looking at 4-1 is in hours so we’re doing hours and then we’re integrating and we’re integrating this.
S of T is in kilometres per hour so s of T is kilometres per hour and DT has a unit remember that is.
The tiny tiny tiny width so that’s in hours so if you are just to integrate speed you would end up with kilometres per hour times hours and that would give you kilometres that’s what you would expect okay you would.
Expect to go backwards from a rate to an amount so it’d give you the number of kilometres but I don’t want kilometres I want kilometres per hour still because I want an average speed so that is going to be those reducing right so we end up with.
Kilometres per hour so the unit’s do match and that that’s kind of a big deal.