Hello everyone, welcome back to a new video.
In yesterday's video, we did time, speed and distance.
Today, we will do new topics ahead of that.
Till yesterday, we did the main formula related to speed is
equal to distance upon time.
And then we did conversion in units.
I told you two standard units of speed.
One was kilometer per hour and the other was meter per
second.
Accordingly, we also solved the question.
In today's video, we will do other types of speed.
First, we will do average speed.
What is average speed?
We had studied the chapter of average.
Sum of all observations upon total number of observations
is average.
Similarly, what will be average speed?
Average means we have different distance and time.
Accordingly, we will get different speeds.
If we take average of that,
Suppose, we have done one distance in a time slot.
Let me tell you with example.
Suppose, we have D1 distance.
What is distance? It is D1.
Suppose, we have done 2 km, 3 km or anything in a time span.
Let us take D1.
Then we have covered another particular distance.
We have covered D1 distance in T1 time.
We have completed D2 distance in some other time.
Suppose, we have done first distance in 1 hour and second
distance in 2 hours.
Similarly, we have different time frames for different
distances.
We have different time frames to cover different distances.
If we see the speed,
For every individual distance,
We have divided total distance in 3 particular distances.
Suppose, we have D distance.
We have divided D distance in 3 slots.
D1, D2 and D3.
We have different time frames for each of them.
So, we will have different speed for each of them.
We will have different speed for each of them.
Because, distance and time are different.
So, if we want to see the total distance,
Suppose, he has covered this distance in 5 km per hour.
He has done this in 6 km per hour.
Then, gradually, his stamina was decreasing.
Suppose, he has covered this distance in 8 km per hour.
His stamina is increasing.
He is warming up gradually.
So, if we have to see the average speed,
What is the average speed?
Every time frame is different.
So, what will be the average speed?
If we sum all these and divide by total distance,
Then, this is called average speed.
So, what will be the formula for average speed?
What will be the average speed?
Average speed means,
If we have to find the average speed,
We can't say that he is walking at 5 km per hour speed.
No.
If we find the average value of this,
Then, we can say that,
He has kept the time and speed in the whole journey.
If we find the average value of this,
What will be the result?
If we sum all these, 5 plus 6 plus 8 is equal to 19.
19 by 3 km per hour.
If we find the average value of this,
Then, it will be 6.33 km per hour.
So, if this is 6.33 km per hour,
Then, what will be the average speed? 6.33 km per hour.
So, this is also close to 6.
This is also close to 6.
And this is also more than 6.
So, if we find the average speed,
Then, it will be 6.33 km per hour.
So, we can say that,
He has covered the distance of 6.33 km per hour.
Right? So, what will be the solution for this?
Either, you can find the speed according to the distance
and time.
Speed S1, S2, S3.
If you find the speed,
Divide it by the number of speeds.
Then, you will get the formula for the average speed.
So, you can find the speed.
Or, you can find the total distance.
What will be the total distance?
D1 plus D2 plus D3.
The sum of these will give the total distance.
And so on.
Divide the sum of the parts.
Divide it by.
So, total distance upon total time.
What is the total time?
T1 plus T2 plus T3.
So, this will be the average speed.
Once you find the speed,
D1, D2, D3.
Now, you don't have the value.
But, if we see this.
Suppose, this is 5 km distance.
1 hour.
So, let's see for everyone.
This is 5 km distance.
Time taken is 1 hour.
This is 6 km distance.
Time taken is 1 hour.
This is 8 km distance.
In how many hours? 1 hour.
Right? So, this is D1, D2, D3.
It is the same as it is.
19 will be the sum.
Divide it by T1 plus T2 plus T3.
That is 1 plus 1 plus 1.
It will be 3.
So, this will be the same.
So, you can do it in any way.
First, find the speed.
Or, you can do it like this.
Total distance covered upon total time taken.
So, what is the formula of average speed?
Write the new heading.
Average speed.
So, we have the formula of average speed.
Total distance covered upon total time taken.
So, after average speed, the next corollary will be related
to average speed. Till now, we had different distances.
D1, D2, D3.
They can be different or same.
No issues.
So, what we will do now?
Suppose, we have two destinations.
One is destination A.
And, the other is destination B.
One person starts from A to B.
Suppose, this is your home.
And, this is your school.
Okay? If you go to school from home, the distance will be
same.
Suppose, the distance is capital D.
The time taken to reach school from home is capital T.
Okay? Now, you will come back from the same distance.
If you come back from the same distance,
Then, Don't say that,
Ma'am, while going home from school, we travel separately
and come back from different places.
Then, the distance becomes bigger.
In general, you are going to school from home and coming
back from the same distance.
So, the distance will be same.
Distance is same.
But, Suppose, it is morning time.
People go to school in a hurry.
So, what is their speed?
Their speed can be more.
And, when we come back from school, after a long day, or
after chatting with friends, then, our speed becomes slow.
It takes more time to reach home.
So, in this case, if we want to find the average speed,
Average speed.
When do we find the average speed?
When we have the distance.
When our distance is same.
The distance between coming and going.
For example,
A person goes to school from home and comes back from
school.
The distance should be same.
So, when our distance is same.
So, how is the distance same?
If we see the total distance,
The total distance covered by a person or a student, from
home to school and from school to home.
What is that?
Once, he travelled D distance.
Then, he came back.
So, D and D distance should be same.
So, D plus D.
What is the total distance?
In this, we have the total distance.
Total distance is equal to D plus D.
This is for going and this is for returning.
So, we have 2D.
Total distance is 2D.
Let us suppose the speed in the morning was 1 km per hour
and the speed in the afternoon was 2 km per hour.
So the speed is different in both the cases.
We are given speed and distance.
We have to find the average speed in this formula.
I have given you the formula for average speed.
Total distance travelled upon total time taken.
We are not given time but we are given distance and speed.
So if I apply the formula for average speed,
I will get the total distance d plus d divided by time
taken.
Now how do we find the time taken?
We are given speed and distance.
So we can find the time taken from both the cases.
So the time will be distance upon speed.
So the distance is initially d and the speed is 1 km per
hour.
So d divided by a is the time taken by the child to reach
school in the morning.
Then we will add the plus sign because we have to add the
second time as well.
So we will get the same distance upon speed.
So distance is d but now the speed is b km per hour.
So divided by b.
Now if we solve this, we will get 2d divided by d.
If I take common from these two terms, then what will be
left inside? 1 by a plus 1 by b.
d cancels with d.
If I take the fraction of 1 by a plus 1 by b, then it will
come down.
If I take ab, then it will go up.
So after solving this, we will get 2 divided by b plus a
divided by ab.
Now if ab goes up, then 2ab divided by a plus b.
Write a plus b and b plus a.
So with the help of this formula, we derived this formula.
2ab upon a plus b.
So average speed in this case will be 2ab divided by a plus
b.
So what will be given in these questions?
We will be given the speed.
The speed of your going and coming is here.
And when can this formula be applied?
It can be applied only when both the distance are same.
The distance of going and coming are same.
That is why we were able to apply this formula.
Because our d became common out and got cancelled.
So this becomes 2ab upon a plus b.
In this, what do we have? Speed.
And what is b? Speed.
This is the speed of going.
From which speed are we going?
This is the speed of going and this is the speed of coming.
Did everyone understand this much?
So these were the two formulas related to average speed.
This was the corollary.
With the help of that formula, you can derive this.
If you are not given time, then with the help of speed, you
will be given speed.
It means that you will be given a hint in the question.
With the help of which you can derive this.
Whatever is required, you can derive.
Now moving on to average speed.
Next if we see,
Next comes the concept of relative speed.
But before relative speed, I would like to tell you one
thing.
What is the main formula we have done?
Now we have studied the ratio-proportion.
Or if you will see that video later on, or if you have not
seen it yet.
So once I made you do the ratio-proportion.
About inversely proportional and directly proportional.
If two quantities, let us suppose we have A is directly
proportional to B.
A is directly proportional to B.
It means that the changes in A will be similar.
B will have a scalar multiple.
It means that something big or small.
If A increases, then B also increases.
A will decrease.
The changes with A, increment or decrement.
The same case will be with whom?
The same case will be with B.
So we used to write this.
A is equal to any constant.
Let us suppose it is a constant.
Small k.
A is equal to constant into B.
This is your directly proportional.
And what was inversely proportional?
A is proportional to 1 by B.
Inversely proportional means it is reciprocally
proportional.
So if A increases, then B decreases.
What is there in this?
Inverse relation.
Inversely proportional.
So we write this as A is equal to k into 1 by B.
That is A is equal to k by B.
Where k is any constant.
So this is about directly proportional and inversely
proportional.
So if we take the same cases in this formula.
So what will be the cases?
So see case 1.
Case 1.
Case 1 is when our distance is constant.
When distance is constant.
Means if we have two cases.
Speed, time and distance of both are given.
Means if we have S1, D1 and T1.
In case, speed 1, distance 1 and time 1.
In case of time 1, speed 2, distance 2 and time 2.
We have two cases.
So what is given in this?
In both, D is constant.
Means D1 is equal to D2.
Both have constant value.
Both have constant D.
So if we take D constant.
D is equal to.
For constant, we take small k.
If it is constant.
So what happens here?
S is equal to k by T.
S is equal to constant upon time.
So see here.
Is it related to inversely proportional case 2 or not?
It is analogous to this.
It is similar to this.
So we can write it like this.
S is inversely proportional to T.
You will not say inversely proportional to 1 by T.
Because it is directly proportional to 1 by T.
But if we see in respect of time.
If we see in respect of time.
So what is in respect of time? It is inversely proportional.
Means as our speed increases.
Then we will take less time.
If we are going fast.
Then it will take less time to reach there.
And if we are going slowly.
Then obviously it will take more time.
That is why this relation is formed.
Speed is inversely proportional to time.
When speed is inversely proportional to time.
So if we see the ratio.
Put this question in this case.
What happens in this?
Speed 1 is equal to distance 1 divided by time T1.
Speed 2 is equal to d2 upon T2.
Now distance is constant.
So d1 and d2 are same.
So we will cancel them out.
If we divide.
S1 divided by S2.
So d1 and d2 are cancelled.
This T2 will go up.
So if we do S1 divided by S2.
So what will happen in that?
This T2 will go up.
T1 is down.
So this will be T2 by T1.
This is our relation.
S1 divided by S2 is equal to T2 divided by T1.
When will this case come?
See in front of S1 there is another time.
Because that is inversely proportional to time.
Inversely proportional.
Okay.
So this S1 divided by S2 is equal to T2 divided by T1.
When will this case come?
So what is the distance in both the cases?
It is same.
Distance is constant.
So one case is done when distance is constant.
Similarly you can do the remaining three cases.
What all can happen?
When time is constant.
Then what relation will be formed?
When speed is constant.
Then what case will be formed?
case 2, case 2, case 2 when speed is, is constant.
jab hum aap speed constant ho jayegi, matlab s is equal to
d by t hota hai, toh t ko agar hum idhar le gaye, speed toh
constant hai, speed ko hum k le lete hain, constant, toh t
k is equal to d, toh isse kya relation aaya humare paas, ye
kiske similar
hai, isse wale case ke similar, directly proportional wale
case ke similar, toh humare paas kya ho gaya, d is directly
proportional to time, when speed is constant then our d is
directly proportional to time, toh agar aap isko aise
karenge d1 by d2, ye
kiske aayega, d1 ke saath, kyoki wo directly proportional
hai, toh d1 ke saath hi t1 aayega, aur d2 ke saamne kya
aayega t2, toh ye aapka ban jayega relation, when our speed
is constant, got it, easy tha ye toh, case 3, when time is
constant, case 3,
when time is constant, when time is constant, toh kya ho
jayega, s is equal to d by t, t ke jaga k lik dijiye, toh
ye kya ho jayega, s into k is equal to d, toh kya ho gaya,
ab s is directly proportional to d, directly proportional
to d, toh same kya
ho jayega, same s1 by s2 is equal to d1 by d2, ye ho gaya
aapka third case, ye tha aapki formulae se related, next
hum karenge relative speed,
I think hume relative speed new video mein karna chahiye,
kyoki wo ekdum fresh tha topic hai, toh next video mein hum
karenge relative speed ka concept, tab tak aap padti
rahiye, practice karti rahiye, thank you. Hey, have you
heard about the refer and
earn program on pure professional?
No, I haven't.
What's it about?
Basically, if you refer the certificate course in HR and
admin to your friends and they sign up using your referral
code, you'll get some awesome rewards.
That sounds interesting.
For every friend you refer, you earn points that you can
redeem for discounts or even cash rewards.
Count me in. I'll make sure to spread the word to all my
friends.