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# Displacement from time and velocity example

Worked example of calculating displacement from time and velocity. Created by Sal Khan.

Video transcript

Let's do one more example dealing with displacement, velocity and time. So we have: If Marcia travels for 1 minute at 5 m/s 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, 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, cuz this cancels out... ...you get displacement, and I'll flip this around I'll write...what's on the righthand side I'll write on the left so you get displacement is equal to time times velocity or velocity times time is equal to velocity times time or velocity times change in time so over here they're asking 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 can do that as her change in time it really is her change in time whatever...you know...if it said 0 minutes on her stopwatch when she started at the end it'll say 1 minute or if it starts at 5 minutes, or maybe it was 3:05 when she started, it'll be 3:06 when she finish it was really the change in time once again, I won't write the delta there, just cuz it keeps it...this is the way you 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, the 't' right over here is one minute... ...one minute... ...at 5 meters per second to the south this right over here is the velocity they give us the magnitude, which is 5 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 5 meters per second to the south so we might just say, hey if we want displacement that's just going to be equal to 5 meters per second to the south times 1 minute the problem here is, when we talk about displacement we're going to think about a magnitude of how much its 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 and a second so you can't just say you're going to get 5, and have some weird thing here so in order for it to all work out you either have to convert the 5 meters per second to meters per minute or let me phrase it in another way you have to convert the 5 meters per second to some amount of meters per minute not 5 meters per minute, it's going to be different or you convert the 1 minute to seconds so at least in my mind it's easier to convert 1 minute to seconds so let's do that so this is the same thing 1 minute times... and we want to get rid of the minute, the minute is essentially the numerator right now we can put this over one but it's essentially the numerator so we want to divide by minutes 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 1 minute and so you have a minute canceling out with the minutes and so now you have 5 meters per second to the south times 60 seconds this is now cool, cuz you now have seconds and seconds I wrote 'sec' there, but this is also 'sec' so now you have seconds over seconds, those cancel out so your displacement is going to be equal to 5 times 60 and then your units left are meters all the time units have canceled out and it's meters to the south and this is equal to...5 times 60 is 300 meters to the south and we are done, that's how much she has been displaced if they just wanted the distance, you can say that she traveled 300 meters just that part, the magnitude of the displacement... ...that is the distance that she traveled