Position Time Graph - Motion in a Straight Line Video Lecture - Class 11

hello friends this video on motion in a
straight line
part 5 is brought to you by exam feel
calm no more fear from exams please make
sure that you have watched part 1 - part
4 before going ahead with part 5 now
very similar to distance time graphs
let us now look at position time graphs
position when we talk of position I mean
displacement now let we will take the
same example and try to plot the
position time graph so that you can
understand the difference between the
two even here
Ronny will travel from his home to
McDonald's let me write here position
time graph is nothing but displacement
time graph now even in this case let us
suppose the distance everything all the
data remains the same the distance
between his home and McDonald's is 2
kilometers
he takes 2 hours to cover the his 2
kilometers
he takes 2 kilometer 2 hours to cover 2
kilometers now suppose Ronny goes from
his home to McDonald's and then again he
comes back from McDonald's to home now
we have to plot the position - in graph
let us look at the graph even in this
case x axis would be time and the y axis
would be position or displacement
whatever you quality now in this case we
see that Ronnie traveled 2 kilometers in
two hours while going from home to
McDonald's he again traveled 2
kilometers in two hours while coming
from McDonald's to home but now we are
talking of position or displacement and
we know that displacement is a vector
quantity
now vector quantity means it has
Direction also so direction is also
there in this case when he traveled from
home to McDonald's the direction was
this when he traveled from McDonald's to
home the direction was opposite correct
now we will launch the graph so in the
first two hours that is this is the
first one our next one hour so the first
two hours he traveled two kilometers so
this is my first point while coming back
he again traveled two kilometers in the
next two hours so next two hours one two
and he traveled two kilometers but in
the opposite direction so instead of
moving in this direction he traveled in
opposite direction so it will come back
in this direction that means the graph
would be something like this that means
he traveled two kilometers in first two
hours again he traveled two kilometers
use if you see it is again one to two
kilometers in the next two hours but in
the opposite direction so I hope now it
is clear between the distance time graph
and the position time graph distance
time graph will not take into
consideration the direction of motion
but the position time graph will take
into consideration the direction of
motion of the object now we will discuss
the slope of position time graph very
similar very similarly with the way we
discussed the slope of distance time
graph now we will take the example of
this graph which we plotted out here let
us suppose we have a graph like like
this so now what would the slope of this
graph do note as we already proved in
the previous case slope of this curve
would be nothing but velocity
when we talk of slope of distance time
graph that is speed when we talk of
slope of position time graph that is
velocity a very easy way to remember is
speed is scalar distance the scalar
velocity is vector position is now in
this case the slope of this graph would
be velocity now let us see how to be
calculate the slope of this graph now it
has two straight lines one two so let us
suppose first we find the slope of this
line then we find the slope of this line
let us suppose this angle let us join it
let's let us suppose we calculate the
slope one that means the slope of this
line now the slope would be equal to tan
theta1 where we considered that this
angle is Theta 1 so this will be equal
to BI by X which is equal to 2
kilometers by 2 hours so this would be 1
kilometer per hour so the slope of this
line would be 1 kilometer per hour
or the velocity till this point would be
1 kilometer per hour now we will
consider the slope 2 that means the
slope of this line this would be equal
to tan theta 2 let us suppose this angle
is Theta 2 now basically when we
calculate slope that is when we
calculate tan theta we take the and we
measure the angle always in
anti-clockwise direction like here we
measure the angle as
tell one so here the angle which we
should measure is this angle now what
will be this angle this angle would be
180 minus theta 2 correct so that means
this the slope of this curve would be
tan of 180 minus theta 2 so that will
come out to be minus tan theta 2 these
are all simple trigonometric relations
now minus tan theta 2 would be minus tan
theta 2 would be y by X so this will
again be minus 2 kilometers by 2 hours
so this will be minus one kilometer per
hour therefore that so the slope of this
line is one slope of this line is minus
one now for the entire journey the slope
would be slow one plus slope 2 that is 1
minus one which is equal to zero so what
do we find in the entire journey the
velocity that is the slope is equal to
zero so what does that signify that
means when the we could squeeze already
saw in the figure that when wrongly
traveled from home to mcdonnell's and
any again came back to home the net
velocity was 0 so we proved the same
thing even graphically that is even from
the position time graph we proved the
same thing just to clear your confusion
here I guess I missed 2 right here that
slope 2 would be tan of 180 minus theta
which would be equal to minus tan theta
2 that
so we will quickly review this we saw
that we know that the velocity would be
the slope of this cut so the slope for
the calculating slope we first
calculated the slope of this line then
we calculated the slope for this line so
slope man worst and theta1
let us Y by X which is equal to this
slope to was tan of 180 minus theta 2 so
that is equal to minus tan theta 2 that
is equal to this now the in total slope
would be slope 1 plus slope 2 which
comes out to be 0 that means the
velocity in this case will be equal to 0
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