Hello everyone, welcome back to a new video.
In today's video, we are going to continue the concept of
time, speed and distance.
Today, we are going to do problems based on train.
Till now, we have seen the formulas of relative speed and
average speed.
Now, what is the difference in the problem of train?
In the last video also, we had done a question on train.
But what was the difference in that question?
We were not given any specific length of train.
In today's question, we will be given a specific length of
train.
Then, we will see the distance, speed and time that we will
use in today's video.
So, let's start.
First of all, what should we remember in the form of speed,
time and distance?
We should remember the same formula that is distance is
equal to speed into time.
Or speed is equal to distance upon time.
What did we remember?
Speed is equal to distance upon time.
So, we should remember this type of formula.
Then, we saw the conversion.
If we want to go from km per hour to m per second, then it
becomes 5 upon 18 into x m per second. This was our formula.
So, we will use this formula.
If we see the concept of train,
I will tell you the main types of problems.
For example, we have a train.
This time, we will be given a specific length of train.
Suppose, we have a train.
This is our train.
So, we will be given a length of L.
Then, we will have cases.
What are the cases?
Whom is the train passing?
The first case is that if a train is crossing a pole, a man
or any other thing, then that thing will be stationary.
Stationary means it would be at rest.
It would not be moving.
It would be at rest.
And the train would be moving at some speed.
So, the first case is when a train is crossing a stationary
body or object.
Then, what is the distance?
If a train is crossing it, then the train has to cross its
entire length.
As soon as it passes, this is the starting point and this
is the ending point of the train.
So, the train will cover the entire distance.
We mean the ending point of the train.
So, the train covered the entire distance.
Suppose, the pole is here.
The train starts from here.
So, the distance covered by the train is the length L.
The length of the train covers the distance.
But, let us suppose that you had a pole at a distance.
So, the length L has to be added to the given distance.
If the distance is a, then in the second case, when the
pole is here, then the distance travelled by the train will
be added to the given distance.
So, in this, earlier we were not given the length of the
train, so we did not add anything.
But, in this question, the length of the train is
specified, so we have to add it to the given distance.
If it is in meters, then meter.
If it is in kilometers, then kilometers.
Similarly, the distance travelled by the train will be
added to the same distance.
So, in both the cases, you must have understood that what
we will do.
We will just add the length of the train to that distance.
So, the first case is when the train is crossing a
stationary object.
When train is crossing a stationary object.
Stationary object is negligible in comparison to the length
of the train.
If you see the length of the pole, it is very less in
comparison to the length of the train.
The length of the man, the length of the tree or the length
of the signal is very less.
So, there will be no difference in the length of the train.
The distance is related to the length of the train.
Now, if we see the next case, If we have a stationary
object, but if the length of that stationary object is very
less, then what we will do in that case?
So, what will happen in the second case?
When a train is crossing a stationary body of some length.
The train is still crossing the stationary object.
It is not moving, it is just stationary.
But now, what will happen to that object?
It will have a length.
In this case, we have a train.
This is our train.
Its length will be L.
Now, what is it doing?
It is crossing a bridge.
So, the length of the bridge will also be very less.
Think of a bridge.
Think of a tunnel.
Its length will also be very less.
So, it is crossing a bridge.
Or a stationary object.
A bridge is stationary.
A tunnel is stationary.
Both are stationary, but it is not moving.
So, it will also have a specific length.
Let us suppose that we have a length.
So, what will be the distance formula for this?
We have to add up the distance of the train.
Now, another distance will be added up.
That is the distance of the bridge.
So, what will be the distance now?
In this case, what will be the distance?
Length of the train will be L.
Plus length of the bridge.
Or the tunnel.
Or any stationary object.
We will have to add up its length.
In order to find the distance.
Total distance.
If we had been given this distance as well.
That is, it is travelling such a distance.
Then, it is entering the tunnel.
It is crossing the bridge.
Then, we would have added up that distance.
So, this is the second case.
When we have a train crossing a stationary object.
And we are given a specific length of the stationary object.
So, this is the second case.
Now, the third case.
Now, we have talked about stationary objects.
And we have discussed all the cases.
Whether it has a length or a negligible length.
Now, we have come to the topic of moving bodies.
Moving objects.
Or bodies.
Now, we have a moving train.
The train was moving in the earlier cases as well.
But, what we are seeing next to it.
Instead of a stationary object, what has happened? Moving
object or moving body.
So, what will happen in that case? Now, you remember a
little bit of the previous video.
When we have two moving bodies.
So, what we had then?
We had speed.
Instead of using normal speed.
What type of speed did we use?
We used relative speed.
So, whenever we have two moving bodies.
Two, three or how many ever moving bodies.
We do not use normal speed.
We use the concept of relative speed.
So, what was your third case?
This was your third case.
When train is crossing a moving object.
What will happen then?
Moving objects.
Then we will have the concept of speed and relative speed.
Then what will happen in distance?
In distance, we will add up the length of the train.
And if moving object.
Let us suppose, what can be the moving object?
There can be two cases in moving object.
This is our train, in which we have to question.
And the other moving object, if it is also a train, then it
will also have a good length.
Then what will happen in distance?
What will be the length of both?
L1 is length of train and L2 is length of train.
So, what will be the length of both?
We will add up with the rest of the distance.
Even if it is another distance.
And if it is this, then we have to add up the length of
both.
Now, it is the turn of speed.
In that, we were not doing anything in speed.
Because in that, speed was only one moving object.
So, speed was of that only.
Now, in this, there are two moving objects.
So, for two moving objects, what will we have?
Relative speed.
Then, in relative speed, there will be two sub-cases.
What will be the two sub-cases?
That the two moving objects are in one direction or
opposite direction.
So, you will use those two cases.
If the two moving objects are in same direction,
Same direction means, they are moving in one direction only.
So, in that case, what will be the relative speed?
If it is x km per hour and it is y km per hour,
So, what will be the relative speed?
In this case, our relative speed will be add up.
x plus y km per hour.
When two moving objects are in same direction.
And what will be the second case?
When two moving objects are in opposite direction.
Then, what will be the relative speed?
Then, the relative speed will be subtraction.
That is, x minus y km per hour.
When we are coming near,
Sorry, sorry, this is another case.
When we are coming near, in opposite direction,
Then, it will be add up.
And in same direction, what will be the subtraction?
Because, when we are moving in same direction,
When we are moving in same direction,
Then, it will be subtraction.
Let's take a mod.
Then, it will be subtraction.
And when we are moving in opposite direction,
When we are coming near each other,
Means, we are moving in opposite direction,
Then, it will be add up.
Because, we think that things are coming close.
So, this is your relative speed.
So, we will see the length in this.
We will add up both the lengths.
If both the objects have the same length.
Suppose, this is not L2,
There is something else in its place.
And, it does not have the length.
Then, we will not add it.
But, it is moving.
So, it will have the concept of relative speed.
For example, if it is a man,
Then, it does not have any length.
So, we will only change the speed.
And, we will add up the distance of the train.
And, we will add up the given distance.
So, let's see the questions on the basis of these.
So, let's see.
First question.
Read it once.
A 20 meter long train,
The length of the train is given.
A 20 meter long train,
Takes 10 seconds to cross a man.
10 seconds to cross a man.
Standing on a platform.
There is a train.
What is the length of the train? The length of the train is
given.
120 meters.
That is the length of the train.
This is a train.
Who is it crossing?
It is crossing a man.
Who is standing on the platform.
So, if a man is standing on the platform,
Then, what is the object of the object?
Is it a moving body or a stationary body?
If it is a stationary body,
Then, the man is standing on the platform.
And, it does not have any length.
It is a negligible length.
So, the length of the man is not given.
So, what is the case of stationary body?
The first case is,
When the train is crossing a stationary body.
And, the body has no length.
It is a negligible length.
So, this is the first case.
So, what is the distance in that case?
The distance of the train is the same.
There is no extra distance.
So, the train is crossing the platform.
So, we will take the same distance.
That is distance in this case.
So, what is the distance in this case?
There is no distance.
So, the length of the train is 120 meters.
Because, there is no extra distance.
So, the train is crossing the platform.
So, this is the case.
When the train was crossing the platform, The train is
covering its length.
So, the length of the train is 120 meters.
How many seconds are you covering? 10 seconds.
So, what is the time? 10 seconds.
So, what is the speed of the train? We are given the
distance and time.
So, we can calculate the speed.
Speed is equal to distance upon time.
That is 120 meters.
First, see that the unit is same.
So, the speed should be meter per second.
So, meter is the distance and second is the time.
So, we don't need to change this.
So, 120 divided by 10 meters and 10 seconds.
That is 12 meter per second.
So, we have the speed of the train.
So, this is our answer.
You must have understood.
This was the easiest question.
Because, the man was stationary.
He also didn't have any length or speed.
So, we didn't have to do anything.
Neither relative speed nor anything else.
Please note down.
Let's see the next question.
Please read.
Next question is,
A train passes two bridges.
Which bridge is the train passing?
Two bridges of lengths 800 meters and 400 meters.
Now, see which case is this?
What is the object of the bridge?
Moving or stationary?
Stationary.
And, its specific length is also given.
See, one is 800 meters and the other is 400 meters.
So, which case is this?
The second case that I told you.
When we have a specific length of stationary object.
So, what is this?
A train passes two bridges of lengths 800 meters and 400
meters.
In 100 seconds and 60 seconds respectively.
There is a train.
It is crossing the first bridge.
What is the length of the first bridge? 800 meters.
And, what we have to find out?
The length of the train.
Let's name it as L.
And, the same train is crossing the second bridge.
What is the length of the second bridge?
The length of the second bridge is 400 meters.
And, the time for the first bridge is 100 seconds.
And, the time for the second bridge is 60 seconds.
So, the length of the train is?
Do it.
How will you do it? If you see that the train will move
from here and will cross this bridge and this bridge.
The distance will be different in both the cases.
Because, here is the bridge of 800 meters and here is the
bridge of 400 meters.
And, the time is also different.
So, one thing will be same in both the cases.
What will it be?
The constant thing that is moving in this case.
What is that constant thing?
The speed of the train.
The train will move with the same speed all the way.
Till we are not given that it is moving with different
speed when we calculate the average speed.
Now, it is moving with the same speed.
So, the thing which will be same in this, that would be the
speed of the train.
So, let the speed of the train be?
Let the speed of the train is equal to?
In meter per second, let us take unit in meter per second.
So, let us take x meter per second.
x meter per second.
You see, you take two cases.
Once the train is crossing this bridge, that case is done.
Once the train is crossing this bridge.
So, we are given the distance.
What will be the distance for this case? d1 distance.
train length will be added and bridge length will also be
added, so it will be L plus 800 meters.
What is L? Let the length of the train be meters.
Length is equal to L meters.
So this will be our distance 1 and time taken is 100
seconds.
So the speed will be S.
Speed will be same in both the cases.
So what will be the speed? Distance upon time will be L
plus 800 divided by 100 meter per second.
Now do the same case 2 for bridge.
For this what will be the distance? Length of the train
plus length of the bridge.
So this will be
L plus 400 meters.
And what is the time given? Time given is 60 seconds.
Speed is same in both the cases.
What is the speed? Take x or S.
So what will be the speed? Speed is same in both the cases.
That is d2 upon d2 L plus 400 divided by 60 meter per
second.
So in both the cases, if you are saying this is equation 1
and this is equation 2, then equation 1 is equal to
equation 2 because both are giving us speed of the train.
So equate both the cases.
If we equate both the cases, then L plus 800 divided by 100
meter per second is equal to L plus 400 divided by 60 meter
per second.
So what will happen? 0 to 0 cancel.
Now cross multiply.
This will be 3L plus 2400.
And this will be 5L plus 2000.
Take 3L here and 2000 here.
So this will be 2400 minus 2000 is equal to 5L minus 3L.
So this will be 400 is equal to 2L.
Divide by 2, so L will be 200.
And what was the unit of length?
Meter. So this is 200 meters.
So the length of the train is 200 meters.
So this is your answer.
It was easy.
You can see which constant is remaining.
So it will be equal.
Equate and find out unknown value.
So this is our answer.
This was the example on second case.
Now let's see next question.
Next question is, read it once.
Next question is, a train 150 meter long is travelling with
a speed of 36 kilometer per hour.
If a man is cycling in the direction of a train at 9
kilometer per hour.
We saw in first question, man is standing at the platform.
Standing means he is stationary.
In this, the man is cycling.
That is, man is a moving body in this example.
So man is a moving body.
So which case we have? This is case 3.
When we had two moving objects.
The second object with the train was also moving.
And when we talked about two moving objects, what was the
speed of that object? We used the concept of relative speed.
So in this question also we will use
the concept of relative speed. So what is given for man?
This is man. He is cycling.
So this man is cycling in the direction of the train.
What does it mean? In the direction of the train means in
the direction in which the train is moving, he is also
moving.
So what is the example of relative speed? When both the
objects are moving in the same direction.
And what is the speed of man? 9 kilometer per hour.
When both the bodies move in the same direction, then in
that case, what is the relative speed? Relative speed is
added or subtracted.
Relative speed is subtracted.
So the speed of the body will be 36 kilometers per hour
minus 9 kilometers per hour.
Because both have the same unit, kilometer per hour,
kilometer per hour.
So there is no need to make any changes.
So what will happen? 36 minus 9 kilometers per hour.
This is our relative speed.
That is 27 kilometers per hour.
This is our relative speed.
Now, the length of the train is 150 meters.
The time taken by the train to pass the man is, means
obviously the speed of the train is more and the speed of
the man is less.
So our train will cross this man at one point. So we are
asked what is the time? Speed is given.
What will be the distance? If the train is starting from
here, then it should cross to the end of the train.
So what will be the distance? In this case, guess, the
distance will be the length of the train.
And the rest of the length is not given.
So the length, means the man and his train are starting
from here.
So what is the distance?
Length of the train, that is 150 meters.
Then the time taken by the train to pass the man is,
When we get the relative speed, we get the distance.
If the distance is speed, then what can we get? We can get
the time.
So take out the time.
What will be the time?
Distance is equal to speed into time. And time is equal to
distance upon speed.
So the distance is 150 meters. Now what is this? 27
kilometers per hour.
This is 27 kilometers per hour.
I hope
I will write it down. This will be 27 kilometers per hour.
We will change it to 27 into 5 by 18 meters per second. Now
cancel out this.
What will be the result? 9 times 2 is 9 times 3. So this is
15 by 2 meters per second.
Is our relative speed. So distance is equal to speed into
time.
So the distance is 150 meters. And the speed will come
down. That is 15 by 2 is equal to time.
2 will go up. This is 1, 10. So what is this? 20. What is
the time? 20.
And what will be the unit? Meter per second. And there was
a question in meters.
So what will be the time? We have 20 seconds.
So in how much time will the train cross the man? In 20
seconds.
So the answer is 20 seconds. I hope this question will be
clear to you.
Is there any next question? There is one more question.
We have done it with three cases.
Three cases means relative speed one also stationary body,
moving body.
The last question we did was related to the relative speed
question.
That is, when both the objects are moving.
Now, both the objects were moving, but the length of the
man was not given because it was not considerable.
We were only given the length of the train.
Now, read this question.
This is your second category, when we are given the length
of both the moving objects.
So, read the question.
Two trains with lengths of 126 meters and 119 meters
respectively are moving towards each other.
That is, this train is one and this train is the other.
Both are moving towards each other.
So, which direction is this?
Both are moving towards each other.
There are two moving bodies.
That means, we will use the concept of relative speed.
For relative speed, we have to look at the direction.
That both are moving in the same direction.
Or in the opposite direction.
In this case, they are moving in the opposite direction.
One is going east and the other is going west.
That means, it is in the opposite direction.
So, in this concept, what will be the relative speed?
Relative speed will be added.
Whatever will be the speed of both, if we add it, we will
get the relative speed.
So, what is the length of this train? 126 meters.
And what is the length of the other? 119 meters.
Their speeds are 12 meters per second and 23 meters per
second respectively.
So, what is this?
First one has 12 meters per second speed and the other one
has 23 meters per second.
So, what is the relative speed with the help of both?
Relative speed is the sum of both.
That is, 12 plus 23 meters per second.
What is this? 35 meters per second.
Relative speed is 35 meters per second.
Now, what will be the time needed by the train to cross
each other?
Time needed by the train to cross each other.
Distance is given.
Relative speed is taken out.
Now, what will be the distance with the help of both?
Distance.
When there were two moving objects with a good length, what
will be the distance with them?
Add up the length of both.
126 meters will be added and 119 meters will be added.
Rest, no extra distance is given between them.
Only length is given.
So, what should we do with them?
Add up the distance.
So, we will get the distance.
Solve the distance.
This is 5.
Carry 4.
So, we will get 245.
Distance will be in meters.
So, distance is here.
Relative speed is here.
So, take out the time.
I will write here.
Distance is equal to speed into time.
So, distance will be equal to speed.
That is 245 divided by speed which is 35.
This would be unit.
Both are same.
Meter and meter per second.
So, time will be in seconds.
So, solve this.
What will be the result? 5 x 7. And what will be this? 5 x
4. 4 x 4 and 45.
9 x 9.
7 x 1.
7 x 7.
So, what is the time? 7 seconds.
This was very easy.
Isn't it?
This question might be looking easy to everyone.
So, 7 seconds.
How much time will it take both trains to cross each other?
Would be 7 seconds.
So, I hope you would have understood all the cases with the
help of these questions and the previous theory.
And you will be able to solve any questions based on these.
So, keep practicing these questions.
See you in the next video.
Thank you for watching the video.
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