Hi, in the last session we did the concept of Relative Speed. In this session we will be doing its

applications in trains, and boats and streams. So let’s take a situation, we will try and calculate the

time taken by a train to completely cross this object which is an object of negligible width. Right, the

object could be a man, a pole or a tree. In this case it is a pole, as you know time taken to cross is

nothing but distance covered upon the speed. So what really would be the distance covered to

completely cross this particular pole. So let’s say I was standing with a stop watch actually

calculating the time. When do you think I will start my stop watch? When the front end is just

touching the pole, am I right, or just coinciding with the pole, right now. And when will I stop it,

when the rear end is just leaving the pole, right. In this time duration how much was the total

distance covered by the train. As you can see the distance covered is nothing but the length of the

train, if I compare the front ends of the train before and later, the distance covered is nothing but

the length of the train, right. And since there is just one object moving which is the train, the speed

would be nothing but the speed of the train, right. So time taken for a train to completely cross an

object of negligible width will be nothing but its own length upon its speed, right. Now, what if this

object was not an object of negligible width, but it had some substantial width, like a bridge or a

platform, or a river. In this case it is a bridge, right, once again time taken is nothing but distance

covered upon the speed, right. Let’s now again come back to the stop watch, the train will be

crossing the bridge, this is where we will start the stop watch, right, when it is just entering the

bridge, and we will stop the stop watch when the rear end is just leaving the bridge, right here, right.

And now if you realise the distance covered by the train to completely cross will be nothing but the

width of the object, which in this case is the bridge plus the length of the train, right, width of the

object plus the length of the train. And once again it is only the train that is moving. So speed will

be nothing but speed of the train. So in order to cross an object of substantial width the time taken

will be nothing but width of the object plus the length of the train upon the speed of the train, right.

Now let’s take another situation altogether, boats and streams, so what we have here is a stream

flowing from top to bottom, let’s say the speed of the stream is b meters per second. Right, on top

of it is a boat which is travelling at a meters per second. So the speed of the boat.