L7 : Distance time Graph - Motion and Time, Science, Class 7 Video Lecture

hello friends this video on motion and
time part 7 is brought to you by example
calm no more pure from exam so now that
we got a good idea about graphs and how
do we draw graphs how do we represent
data in graphs so let us now talk in
detail about the distance time graphs
because these distance time graphs are
going to give us a lot of information
about motion of various objects so let's
look at this example where we see this
little boy is traveling from his home to
McDonald's and then he is coming back
from McDonald's to home so when we try
to represent it in a distance time graph
where we take time on the x axis and the
distance on the y axis now the shape of
the graph tells us a lot of things let's
say if the graph is a straight line so
what does this graph tells this graph
tells that the object travels now let's
see if say the time is in hours and
let's say the distance is in kilometers
so this tells us that the object travel
any point of the any point on this line
tells us the distance traveled in a
particular time so let's say we take
this point so this point on the graph
tells us that in two hours so this is
two hours this object traveled two
kilometers right so that is what it
tells us at this point similarly if you
take this point so this point tells us
so you join these points so this point
tells us that in this is three point
five so in 3.5 hours it track object
traveled 3.5 kilometers so any point on
the line actually gives you information
about the distance traveled in a
particular duration of time so that is
something which you can infer from the
graph so looking at the graph you can
also tell what kind of motion
the object has whether the object is
moving uniformly or the object is not
moving uniformly so all those
information can also be derived looking
at the distance time graph now some of
the interpretation from a distance time
graph our first interpretation is
distance traveled at specific intervals
of time so that means any point of the
graph will tell you how much distance is
being traveled at a particular instant
of time as I was telling you so at this
point you can tell that it traveled one
kilometer in one hour at this point you
can tell that it traveled two kilometers
in two hours and so on so you can
actually tell how much distance has been
traveled at specific intervals of time
so if I just give you this graph and if
I tell you that how much distance has
been covered in in say a time duration
of three hours so this is three hours so
this is three hours so corresponding to
three hours this is the point so for
this point what is the corresponding
distance that is three kilometer so you
would say that three kilometer is
traveled in three hours so each point
represents how much distance traveled in
how much time so with that information
we can actually tell us that when the
car is moving how much it has covered in
how much time now the second
interpretation from a graph could be the
distance traveled as a particular
instant of time let's say if you talk
about so one thing is how much it travel
in two hours right so that is one thing
the another thing is how much it
traveled at say the third hour at the
second hour so if I tell you that how
much distance it had traveled at a
specific instant at this instant of time
how much distance it had traveled so you
can very easily calculate corresponding
to this how much distance has been
traveled another thing is
I tell you how much distance did it
travel between two and three hours so
between these two how much distance is
that traveled so for corresponding to
two let's say it has traveled this much
distance corresponding to three let's
say it has time and three kilometers so
that means basically this much time
duration it has traveled this much do
this much distance that is one kilometer
so basically it has traveled one
kilometer between the second and the
third hour
so all these calculations can also be
done looking at the graph so these
calculations become easier it also tells
us about the speed of the vehicle and
this is very interesting that is how
fast the object is moving from one place
to another and how do we find that
looking at the graph so graphically now
normally what do we know that speed is
nothing but distance traveled per unit
time so that is how we define speed
right but how do we calculate speed
looking at the graph now the slope of
this line tells us the speed of the
vehicle now what is slope slope is
nothing but the stiffness of this line
how steep the line is so this line could
have been something like this the line
could also have being something like
this the line could also have been
something like this so how much slant
the line is that decides the speed of
the vehicle so that's the beauty of this
distance time graph so let's see what do
I mean by that so let's stick to the
previous line that is the blue colored
line so in this line let us say you
assume any particular point you consider
any point let's say I have considered
this point as I say that I want to find
out the speed at this point so what
would be the speed at this point so at
this point how much is the distance
traveled so the distance travelled is 2
kilometers for this call point how much
is the time
the time taken is two hours so what
would be the speed at Point P it would
be distance traveled divided by time
taken so this is going to be one
kilometer per hour so that would be the
speed at Point P so how did we calculate
that is the y-axis divided by the x axis
and what the slope now what did I mean
by slope slope is nothing but the slant
of this line and slope is given by this
divided by this status slope so
basically this is nothing but the
distance traveled and this is nothing
but the time taken correct so that a
slope so slow up in something like this
slope of a line so slope would be like
this let's say this is a straight line
so the slope of if I ask you what is the
slope of this line so the slope of this
line is going to be this divided by this
so that would be the slope of the line
so if this is a this is B and this is o
then slope is going to be a B by Oh B so
that is how we define slope now if this
line is more steep for example in this
case so let's assume this case so in
this case the slope would be something
like this this distance divided by this
distance in this case you see the
numerator is more therefore the value of
the slope in this case would be more all
right so let's see the slope for this is
x1 slope for this is h2 so we will say
that H 2 will be greater than s1 but if
you consider the slope of this line so
this would be this divided by this
correct so if you calculate the slope of
this line so this would come out to be
less so this slope would be less than s1
so if you want you can actually try
calculating this and then you can see
that yes that is how it is
so as the
Lanning becomes more and more steep the
slope increases and slope of the line is
nothing but the speed of the vehicle so
that's how looking at the distance time
graph we can also calculate the speed of
the vehicle thank you
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