Displacement from time and velocity example

let's do one more example dealing with displacement velocity and time so we have if Marcia travels for one minute at five meters per second to the south how much will she be displaced and so we know we know that that velocity let me do it this way we know that velocity is equal to displacement is equal to displacement divided by time and it's really once again it is change in time but we'll just say time that's implicitly change in time and if you manipulate this a little bit you really just multiply both sides by time you just multiply both sides by the variable t you get displacement because this cancels out you get displacement and I'll flip this around I'll write what's on the rights and what's on the right hand side all right on the left so you get displacement is equal to time times velocity or velocity times time is equal to velocity is equal to velocity times time or velocity times change in time so over here they're asking us for displacement they're asking us how much did Marcia get displaced and they're saying that she travels for one minute so this one minute right over here this is her time sometimes you could view that as her change in time or it really is her change in time whatever you know if it said if it's at zero minutes on her stopwatch when she started at the end it'll say one minute or if it started said five minutes it maybe was 3:05 when she started it would be 306 when she finished it was really the change in time once again I won't write the Delta there just because it keeps it this is the way you you'd off you've most frequently see it but I want to tell you that these are the same thing for the purpose of this problem because sometimes you'll see the Delta there so the one minute so the T right over here is one minute one minute at five meters per second to the south at five meters per second to the south this right over here is the velocity they give us the magnitude which is five meters per second or you could say that's the speed and they also give us the direction to the south so this right over here is five meters per second to to the south so we might just say look hey if we want displacement that's just going to be equal to that's just going to be equal to five meters per second to the south to the South times one minute times one minute times one minute the problem here is is that when we're talking about displacement we're going to think about a magnitude of how much it's moved so it'll be a distance of some kind and some direction we have our direction here but we don't want any other units there and if we just multiply this over here we have a minute over here but we have seconds in the denominator you can't just cancel out a minute in a second so you can't just say you're going to get five and have some weird thing here so in order for it to all work out you have to either convert the five meters permit per second to five meters per minute or not or let me phrase that another way you have to convert the five meters per second to some amount of meters per minute not five meters per minutes going to be different or you convert the one minute to seconds so at least in my mind it's easier to convert one minute to seconds so let's do that so this is the same thing one minute times and we want to get rid of the minute and the minute is essentially in the numerator right now we could put this over one but it's essentially the numerator so we want to divide by minutes we want to divide by minute and we want to multiply by seconds we want seconds in the numerator and so what is how many seconds are there per minute you have 60 seconds for every for every one minute and so you have a minute cancelling out with the minutes and so now you have five meters per second to the south times 60 seconds this is now cool because you have seconds and seconds I wrote SEC there but this is also SEC so now you have seconds seconds over seconds those cancel out and so your displacement is going to be equal to five times sixty five times 60 and then your units left are meters all the all the time units have cancelled out and then it's meters to the south so me ders to the to the south and this is equal to this is equal to five times 60 is 300 meters to to the south and we are done that's how much she has been displaced if they just wanted the distance you could say that she traveled you could say that she traveled 300 meters just that part the magnitude of the displacement that is that is the distance that she traveled