Displacement, velocity and time
Displacement from Time and Velocity Example Worked example of calculating displacement from time and velocity
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- 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...
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