# Speed Time Questions Relative Speed YouTube Lecture Handouts

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## Relative Speed

In this class, there are two important topics: Speed and Ratio

Speed

If distance is constant the speed and time are inverse the proportional to each other which means that if one of them is gets reduce the other would increase and vice versa.

Distance

The second think is distance is directly proportional to speed if time is constant so for example, the speed is increase the distance would increase and vice versa.

Relative speed is deal with Boats and Steams

Consider there are two objects A and B would moving each other like cars, boats, trains, etc. the distance between these two objects A and B these to moving objects is the relative distance.

Let՚s say that, object A moves at rate of 2 km ⁄ h and the object B moves at the rate of 3 km ⁄ h. The distance between these two objects or relative distance would change by how much, therefore, the total change

If two objects moving in same directions towards each other in opposite direction then the relative speed is the sum of their individual speeds.

In such as concept, what happens if two objects are moving in same direction?

For example, there are two cars A and B. Car A moving at 2 km ⁄ h and car B moving at 3 km ⁄ h but these time they would be moving in same direction. What would happen after 1 hour?

Let՚s say in 1 hour, our car A would move by 2 km and our car B would move by 3 km so what the relative distance after 1 hour:

## Relative Speed (Opp Direction)

These are the two things would be remember for relative speed. A car travelling in opposite direction the relative speed is the addition of the individual speeds in these guy was they didn՚t do these the relative speed that՚s why the crash.

## Relative Speed (Same Direction)

If these two cars are moving in the same direction, so notice how the distance between these two changes very slowly. It although the two cars they are individual going to very fast but the difference the relative distance between these two, it՚s changing very slowly because it is equal to the relative speed.

## Train a from Delhi to Ahmedabad Left at 2: 30 PM at Speed of 60 Km/Hr. Another Train B Left 2 Hours Later at Speed of 80 Km/Hr. How Far from Delhi Will They Meet?

This is very simple example.

There is a train A which leaves from Delhi to Ahmedabad at 2: 30 PM at the speed of 60 km/hr.

Second train B which leaves 2 hours at the speed of 80 km/hr.

Let՚s see the scenario is after 2 hours, train A moves

Train B able to cover every hour.

So, time

In 6 hours our train B would be able to reduce the distance, the relative distance 120 km to 0 and hence the trains would meet.

Distance

## A Train M Leaves Meerut at 5 Am and Reaches Delhi at 9 Am. Another Train N Leaves Delhi at 7 Am and Reaches Meerut at 10: 30 Am. At What Time Do the 2 Trains Cross One Another?

Here the two trains are travelling in opposite direction.

Two stations Meerut and Delhi, Train M leaves Meerut at 5 am and Delhi at 9 am; Train N leaves Delhi at 7 am and Meerut at 10: 30 am.

Let՚s say, speed of train M and train N

Let՚s find out the time , at which these two train time after 7 o՚clock.

At 7 o՚clock our train M is reached at going in the speed of .

So, time

## Two Friends Started from a to B in the Same Direction Along a Straight Line Simultaneously. The Faster Friend Tim Was on Bike, While Jim Was on Bicycle. The Ratio of Their Speeds Was . Sometime Later Tim Parked His Bike and Started Running Back Towards Jim՚S Bicycle. His Speed Dropped by 80 % . Jim Had Travelled 15 ⁄ 2 Km in That Time. They Meet After 4 Hrs. What Was the Speed of Bicycle?

There two friends Tim and Jim.

We know,

Person of bike, he walking in back speed and cycle person also speed

So, the relative speed and meeting after 4 hrs.

Time

## Ram and Shyam Run a Race between Points a and B, 5 Km Apart. Ram Starts at 9 Am from a at a Speed of 5 Km/Hr, Reaches B, and Returns to a at the Same Speed. Shyam Starts at 9: 45 a. M. From a at a Speed of 10 Km/Hr, Reaches B and Comes Back to a at the Same Speed. At What Time Do Ram and Shyam Cross Each Other? At What Time Does Shyam Overtake Ram?

There are two friends Ram and Shyam.

At 10: 00, Shyam is going in this direction at the speed of , Ram is coming back at the speed of

Therefore, relative speed

They would cross time

So, 10 minutes after 10: 00 they would cross each other.

2^{nd} problem:

Ram would cover

At 10: 15 Shyam just moving at the same direction at the speed of

Relative speed

Distance has to cover

## Arun, Barun, and Kiranmala Start from the Same Place and Travel in the Same Direction at Speeds of 30,40 and 60 Km Per Hour, Respectively. Barun Start Two Hours After Arun. If Barun and Kiranmala Overtake Arun at the Same Instant, How Many Hours Before or After Arun Did Kiranmala Start?

There are 3 people: Arun, Barun and Kiranmala

Their speeds are

After 2 hours Arun, Barun start, relative speed

So, every hour Barun catches 10 km/hr of the 60 km, so total distance

Intersection after 6 hours

So, after Arun and Barun at the same points.

Kiranmala cover

Barun travel for 6 hours or waited for 2 hours

So, Kiranmala wait for

## A Train X Departs from Station a at 11.00 a. M. For Station B, Which is 180 Km Away. Another Train Y Departs from Station B at 11.00 a. M. To Station a. Train X Travels at an Average Speed of 70 Km/Hr and Does Not Stop Anywhere Until It Arrives at Station B. Train Y Travels at an Average Speed of 50 Km/Hr, but Has to Stop for 15 Minutes at Station C, Which is 60 Km Away from Station B en Route to Station a. Ignoring the Lengths of the Trains, What is the Distance, to the Nearest Km, from Station a to the Point Where the Trains Cross Each Other?

There are two trains: station A and station B

A train X departs at 11: 00 am and station B also starting at 11: 00 am

Train X average speed and Train B

Train Y covers time

Individual speed accept 15 minutes train Y not moving at a told.

Train X cover

Subtract

So, is the distance which these two trains are traversing together at the relative speed.

So, how much time would we take them to intersect to make the distance 0.

Hence, the distance

## Next: Problems on Trains and Boats

-Mayank