Understanding Kinematics: Position, Displacement, Distance, Velocity, and Speed

good morning today today today today well today we're going to continue with

our investigation of kinematics and ultimately we'll discuss this video and what it actually means in terms of

this car moving across the screen so let's commence operations

today we'll be specifically discussing position displacement distance velocity and speed

and so referring to your notes please open up your package to this specific page

what is position it's location of an object relative to a reference and it ultimately requires a measurement

of length or distance and direction the symbol in physics

is d notice d has an arrowhead above it that means it's a vector the unit is meters example one

a person is staying five kilometers east of his home the e in the bracket stands for east

and so the home here is the reference point and basically we're saying this person

is standing five kilometers east of his reference point here we have the direction east

and west defined so we would write d equals five kilometers east please highlight this

if you haven't already done so please write down that d or position is a vector

now specifically for this example if we want to state that someone's position

is their initial position then we would use a subscript one in physics sometimes in some textbooks

you'll also see an i subscript so for this person staying five kilometers east of their home

we would say their initial position is five kilometers east that's how we write it

now in this second example the same person has now moved to a new position 13 kilometers east of

their home well specifically if we want to show in physics that a person has

moved to a new position or a final position we normally use the subscript d2

two standing for final so please add these subscripts to your notes d1 equals five kilometers east that's their

initial position east of the reference point the home and d2 is 13 kilometers east

of the reference point or their home now in physics when the position of an object changes we have a specific

name for that if we want to be very specific here we can say that the person has walked

eight kilometers east from their initial position to the final position now the name of

this is called displacement so next we'll talk about displacement and distance

and how they can potentially be different displacement the net travel object as

measured from its starting point to its end point in a straight line more commonly displacement is often

called the change in its position the symbol for displacement is delta d delta mathematics or in physics means

change this symbol is often used in mathematics delta symbol for rise or run

now in our situation d2 was 13 kilometers that was the final position

and d1 was five kilometers that was the initial position and so please fill in this in your notes

for this first example we just did above delta d which is d2 minus d1 the change in position

13 kilometers minus five kilometers equals eight kilometers east notice displacement once again has

this arrowhead and that means it's a vector and so for the above example the

person's displacement is eight kilometers east or delta d and the arrowhead is missing

here so please add it equals eight kilometers east distance there are very few situations

actually where distance and displacement will be the same and we'll discuss those situations

in a few moments however distance is a measure of the total length of path that an object

travels along the symbol for distance is just delta d without the arrow head that means that

distance is not a vector that means that distance does not require direction

that's really important so for the example we just did the distance traveled by the person

was also eight kilometers and we would write delta d equals eight kilometers without any

direction so the only time that distance and displacement will be exactly the same

is when the person is traveling or the object is traveling in a straight line that's it the moment the person deviates

from traveling in a straight line in one direction that's the moment displacement and distance will be

different so keep that in mind displacement is the change in an object's position

if an object's position doesn't change its displacement is zero distance is a measure of the total

length of the path that an object travels along they seem similar and yet there are

slight differences let's look at an example captain canuck is running

a race at a track meet one lap is a total of 400 meters if the captain runs four laps find a the

distance traveled and b the displacement so i think this example will clearly show when

they will these two variables will be different and so here's our track and

let's say that the captain captain canuck here starts at this point starts running around the track runs

again and so on he's running four laps all together

however we're gonna say that captain canuck starts and finishes in the exact same spot

so that's really important to note so the distance is fairly straightforward 1

600 meters if one lap is 400 meters then 4 laps is 1 600 meters the displacement however

is actually zero why is that well remember the definition of displacement

is the change in position has the person's position changed no no it hasn't at all

he started at this position captain canuck and he finishes at the exact same

position so if the position doesn't change then your displacement is zero

for there to be displacement the object's position must change so when you get up in the morning and

you go to school then you come back home your overall displacement for the day is zero

even though your school may be say five kilometers away from your home so you travel in the morning to your

school that's five kilometers you travel back from school to your home that's another five kilometers you've

traveled 10 kilometers altogether your displacement is still zero because your position

from where you started off in the morning at your home to where you end up in the afternoon after you come back at

home your position is the same if your position hasn't changed your displacement is zero

i strongly suggest you try these practice problems these practice problems will reinforce

some of the discussion that we just had and of course

you could find the solution to these practice problems by clicking this link at the website

here is the website and because it's a grade 11 course you would go under grade 11

because we're studying motion you would go into the motion unit and you'd find these links here

with the full solution so if you can't get these answers make sure you click the link found

under 11u physics click these links and it will show you step by step how to do these problems and here's the

website up here all right continuing on please turn to this specific page

in your notes with sign convention in physics when we're talking about displacement or velocity or forces or

any vector quantity in general north is always a positive number and south is a negative number

east is positive and west is negative up is positive and down is negative and finally right

is positive and left is negative so what does that mean well in general if we have a position here

say 10 kilometers north it can be written just as positive 10 kilometers and it would be understood

or just 10 kilometers it'd be understood that that 10 kilometers is right as north so you wouldn't have

to necessarily write down north here in the question or in your solution because positive means north however

if you want to represent five kilometers south this would be written as negative five kilometers and it would be

understood that if you have a negative in front of the number that would mean south

that's what we mean by convention so three kilometers east because east is automatically

by the convention positive it could just be written as three kilometers and it would be

understood that it meant east in terms of reference to the question 10 kilometers south can be written as

just negative 10 kilometers south being understood as being negative please try these other examples now

please pause the video go ahead all right i've assumed you've tried these

questions and here are the solutions five meters up positive five it's understood

two meters down well down is opposite up so we use a negative to represent that and west is opposite east so once again

we use a negative to represent that let's try this question a person walks five kilometers

north and then turns and marches three kilometers south the person stops for a few hours and

then walks two kilometers north how far has she traveled what is her displacement

please pause the video now and give this a try all right i'm assuming you've tried it

so distance is always straightforward distance we just add numbers because for distance

it's not a vector it's a scalar quantity meaning direction doesn't matter it doesn't

matter what the direction is when thinking about distance

and so five plus three plus two that's ten kilometers that's straightforward but for displacement remember we have to

take into account direction and so the formula looks very similar for

displacement however notice notice that when the person has traveled south

we haven't written positive 3 we've written negative three so even though the person's distance is

ten kilometers their displacement is four kilometers that means that they are four kilometers

north from where they started now does this make sense let's see with a diagram

so we start here and we've traveled five kilometers north at this point what do we do

well at this point we turn back around and we've traveled three kilometers south and then after stopping

we travel two kilometers north and so how far are we from where we started

well five then we've gone back three so right now at this point we'd be two kilometers

from where we started but now we travel another two kilometers and two plus two is four kilometers

remember what displacement is it's how far away are you from where you started well

you are four kilometers away specifically four kilometers north from where you started average speed

the ratio of the distance traveled to the total time distance over time or delta d is the

symbol for distance divided by delta t so this is the formula we just used a few moments ago to determine the speed

of the character the unit normally is meters per second or kilometers per hour and so one meter per second equals what

in terms of kilometers per hour well it's 3.6 so the question is how do we get this conversion

we'll discuss that in just a moment now average velocity is the ratio of displacement to the total time

displacement over time so it's slightly different for average velocity you're going to need a direction

and so i promised you that we would discuss how to convert a meter per second into a

kilometer per hour i want to formally show you this it is the final answer is 3.6 but let's

see how we get that so we have to know that one kilometer is 1000 meters

and we also have to know that one hour is 3600 seconds

and so 1 meter per second equals 1 meter per second times a fraction and we want to convert

now it doesn't matter which order we do this in but we'll convert meters into kilometers so we'll use this

ratio here that one kilometer is a thousand meters and notice when we write it like that

the unit of meter cancels out it terminates and so what we're left with is zero

decimal zero zero one but now we're no longer left with meters per second because the meters are gone

we're left with kilometers per second but we don't want kilometers per second we want kilometers per hour

so once again we have to fill in a fraction here and so the question is this we know that

one hour is 3 600 seconds do we write one hour here over 3 600 seconds

or do we write 3 600 seconds over 1 hour well we want kilometers per hour right now we have kilometers per second

so we need hour on the bottom part of the fraction and seconds

on the top part of the fraction so we've just written 3600 seconds over one hour and now notice

when seconds is here and we have seconds there what will happen once again the units

will terminate or cancel and what are we left with

we're going to be left with kilometers per hour and as you can see when we multiply

these two numbers we're left with 3.6 kilometers per hour so that's how we got a conversion of one

meter per second into kilometers per hour 3.6 kilometers per hour

please make sure you copy all this down so one of the questions i always ask my students is what does 40 meters per

second mean because if you really understand what 40 meters per second mean or in general

what the unit of meters per second mean then you don't even need a formula

i know i just gave you the formula speed equals distance over time i know we just saw for the speed of a

character moving in a video game using that formula but if you just understand what this unit means

then you'll never have a problem manipulating the formula so what does 40 meters per second mean

let's say an object was traveling not just at 7 meters per second but at 40 meters per second what does that

actually mean well it means that every one second in this case let's say it was a car a

car would be moving 40 meters so if in one second the car moves 40 meters in two seconds

the car would move 80 meters and in three seconds 80 plus 40 120 meters and in four seconds

120 plus 40 160 meters so if you just understand the unit meter per second or kilometer per hour

you don't even need a formula anymore let's look at this example from your notes

a speed skater travels around the 600 meter track in two minutes and 12 000 milliseconds

find the skater's average speed and average velocity so we're going to use the formula speed

equals distance over time delta d over delta t the distance being 600 meters

time is a bit more complicated on purpose i've mixed up the units i'm a fundamental believer in students

really analyzing what a unit means and so i'm just not going to give you on your test

the unit of seconds you're going to be forced to manipulate these units so two minutes

let's start off with two minutes well two minutes is 120 seconds one minute is 60

2 minutes is 120 12 000 milliseconds well you have to remember what a milli is

a milli means a thousand so 12 000 milliseconds divided by 1000 is 12 seconds

so remember that and if you don't remember that please write that down 1000 milliseconds is one

second a thousand millimeters is one meter remember that so the total time is 132 seconds

and we do our division and we get 4.54 meters per second and that's 5 meters per second in

significant digits why one significant digit because the number 600 only has

one significant digit not three just one i'd like you to now try to get the average velocity

please pause the video now all right assuming you just tried that to understand how to get average

velocity we need to look at a track and one assumption we're going to make is that

the person starts and stops in the same spot so if they start and stop in the same

spot as i go around this track and this track obviously is not the scale it's much smaller than 600 meters

but if the person starts and stops in the exact same spot

then the average velocity is zero why is that well remember the average velocity is

the displacement over time and in this situation we're going to say a person starts here and

finishes in the same position so if they start and stop in the same position that means

the displacement is zero and if the displacement is zero the average velocity

is zero so the last thing i'd like you to suggest please try these practice

problems from your notes the solutions are available online

full solutions with answers and finally at the very beginning we opened with this picture so what does this

picture represent well it represents a very tiny remote control car

moving across this measuring tape at a constant speed and you can see that this distance this white line here is 25

centimeters now a video was used to record the motion of this car

and then images were extracted they were extracted every decimal zero six six six seconds or every one fifteenth of a

second they were extracted and then they were cropped

and this one image was created and the one thing i want you to notice is that the gap from image to image

seems to be very steady and because it's very steady when the gap from image to image is steady we say

that the object is moving with constant velocity and so your task here is based on this image to figure out

the velocity of the car and to figure out the time have a great day bye-bye