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okay today we'd like to look at transformations of
motion graphs, meaning h
how do we convert that into how do we see she politely
this she time graph or an acceleration it's a few tools from going any
in order to be able to do this are we've seen them before
firstly we know that still an X-T graph
we had a XT graft she time graft in the rises tell tax
and Iran is delta T said slow
the sequel to The rise over run top tax
T which we call lost United what's
take any decision time graph
is lost and we can do exactly the same thing
tell us the time graph sure the rise to detail to be
Ryan still 2t said slow is equal to
dealt x over delta T 26 Irish
so anytime we look at DT crash
stop attention give us
scourge she second relationship
we need is related to the area's
graffiti in HD crash and we're not going to be able to do
truth here because it requires calculus but we can show it at least for
some simple cases
Lee are too short for the simplest case so here we got a case we gotta constable
law city its
5 meters per sec and if we contact same speed 25 meters per second
Ford 10 seconds are displaced
will be 50 meters well 50 meters
just area under this cursed
times so we end up generation ship to the area
under GVT
is to T space
and we can do
period our calculation wish 2x
she time grass if for instance
we've got to subject moving see gaining speed
exploration 5 me just
scanning speed at a rate of five meters per second every sec and it does so for
10 seconds
and wanted to do his cane 50 each speech
well that's just the change lost generation shipped or
under any GT crash
is
its Kody equal to Cheech loss
sleeve tees to relationships use
stools said week transform
between the different text ok
first example that we're going to do is he just
polity to example thank you work
downloads sinister the next to crash
and we know that d slope on the next year ***
is equal to value to DT
that's always as we come down is trashed
becomes still XT this loss
stop DT 6 rich dis
used the speech twist
so she called so
lets you take a look at this first church here we've was sitting in with us
total
serious thats user i'd engine
and she start my velocity sir and I've gotta
pasta slow and I moved even more positive so
some in those too much higher colossally
and its spinning at this is problem that would mean that we have a constant
acceleration
I'm going to increased my velocity it costs
rate that means last a straight line
trash show
second region stoked here
key all-time sir answer
value the whole time is in other words
if we're not moving our velocity is she really got a
constant negative the Los specially come
constant naked bad
at this point here we cross the origin by we're doing it at a constant
lost cross now this final reaching here and we're starting out with the fairly
large
pas is slow to
best and its 3 cantors euros
here sigourney end up this year old value
starting out with a high positive value
appear sting that's a problem lost
decrease cost on a cruise ship
and then in the last region
for the last one exploration it's the same game
stock becomes about securities gotta Plaza slow
constant Plaza slow cost last
just so constant value
cost 0 Stoke should I
so here we have sure its operation because the Arctic's
moved curious exploration because removing it cost lost
and here we got a constant negative
so becomes a constant negative
okay let's try another example
this time or use both relationships because we've given up the teachers
so we're going to come down this way and say dat key
still equals value
roster didn't work upwards
to start from the gt2 GT crash
and that's where the area equal
change in the quantity this case to change such
asleep downwards
first its easy one so sure we have
Clark we have is sure a slow response to
value negative so
today I was a slow
Hans just so
throwback she's
sheesh little harder working this way so
let's calculate the area here well I don't have numbers
can be qualitative we've got which kinda posterior its
positive shared fairly large parts to their
so going to go out large
pasta value question becomes
how do we how how do I want to connect and all
one point here its initial position
is given here is nothing about the VT grass to let us know where we're
starting
so they had to tell us the teenage she's
I'm international teach so we gotta go from zero
any creased just despite
just increasing here's really area and rear
then the question becomes what
how do we get there well because it's its constant velocity here
I means our sheet increasing const rage
which streak
now in this region
we've got a positive area here
followed by a negative area and they seem to be pretty much since I said too
soon
this starts what that means is total area
in that region be sir so
there can't be any spaced that beach
next
reach now up to this point he's got a posterior
that means it's going to increase its
decision to the right spied gets to hear
should be a a maximum T-forty kannst
creased this negative your now
now we know that this is it
plastic surgery she in that me instead
discourage will be a problem he can she already did
holtons downwards to where you really know that is
debt we have negative slope here that's a negative x a rich
in a negative acceleration is concave down to problem stamp so
snowed here negative exploration shoes
concave down
sheet grass at Skokie
shaped conch this next period that said
a negative area that's half as big as this
here so starting here
you won't get down all the way the bottom only have how his biggest
prints and negatives just consistent negatory
this is a positive so Cummins we have to be
clunky up courts inside
trouble
in this last region has no area at all
meter to sushi gonna change
stay where it is
towers like costs
10 strike one more
this time we're gonna put some numbers in
come what do both directions again so we're gonna go downwards
where the still you can see I
we're also going to for up for its
ready area is equal to change
quantity sketched change to switch
okay so here's our first region the area would be four
times for times half
step the area she positive
sheet
so once again we have to assume
inferno told otherwise soon decision structure
snatching from the lost the grass tell you
should strike so we'd like to go up
by eight okay so there's 10
short maybe
this year is he negative acceleration texts and negatives separation on the
way to hear
classed X which which
can in fact to Syria here is going to be
negativity so we're gonna end up coming back
to where we started because the positiveID area canceling
negative area no distaste and
reach this negative
slopes negative acceleration to this has to be a concave
down
k'nex region here we've got she area here
for times for City area here
is equal to sixty so we need
and it's an negative area sleep and come down
by 16 units castle grande 0
should and out just past year
sixty has a law cities
constant means artist
space is changing had a const rate
X
where which did down from zero
to -16 because area 26
weekend another area here and it's negative
its -8 Ste come down by
another sheet were at -16
minus another it would be negative when he force MP almost
the past year
okay week positive slow
means plastic celebration
that means we should have trouble at
opens carports its should be
stance no
here
and end the next area is zero
so we're not gonna change ur switch
region family got a
plus 8 so great
-24 we had a
end up -16
thanks here this is a positive so
its should open its
to get there and then finally
the last region here skin straight line
by the time we get 30 seconds that area
here's what's six sixth sense for 24
straining to 16 get up skeet
which its here
T velocities constants space
increase cost
and ask your church
easy one to do here sticks operation cursed
Stoke coming down here
what drops by he -8
in eight seconds Scopus -1
naturally down here and stays still
-1 all the way to its can
and sub-zero value comes here
and slow here is positive one echoes
up 4sec it goes up by fourteen four seconds
Ste pas one
and Dan another 0 slow preachy
and then at a positive one Stoke reaching
and then another sir Ste which
stats were crushed
its summary stock becomes value as you were cancelled just open XT
St law City school need
its DT is screech
stroke beacons values networking
upwards the area under 80
will be to change lost million do an example that
exactly the same examples we did
weeks truck City area under PT
to DT spaced which
to search
and that's all for today folks thank you