In this section, the following topics are discussed with examples

**Basic Formulae****Unit Conversion****Relative Speed****Problems on Trains****Example**

#### Basic Formulae

Distance=Speed * Time

Speed = Distance / Time

Time = Distance / Speed

#### Unit Conversion

• To convert m/s into km/hr:

x m/s = x * (18/5) km/hr

• To convert km/hr into m/s:

x km/hr = x * (5/18) m/s

• If a man covers a certain distance at two different speed x km/hr and y km/hr. Then,

Average speed= 2xy / (x + y)

#### Example 1:

If a person covers a distance of 75m in 2 hrs.What is his speed in km/hr?

**Sol:**

Distance=75m

Time = 2 hrs

Speed=x km/hr

Speed= (75 * 18) / ( 5 * 2 )km/hr

=135 km/hr.

#### Example 2:

If a person covers a distance at a speed of 8/10 of his usual speed he reaches his office 5 minutes late?What is the time taken by him to reach his office?

**Sol:**

s = (8/10) *s

=8/10(d/t)

T=t+5

s=d/t

(8/10) * (d/t) = d / (t + 5)

t=20

### Relative Speed

• If two objects A and B are moving in the same direction with the speed of x km/hr and y km/hr. Then, their relative speed is,

**Relative Speed=(x-y)km/hr**

• If two objects A and B are moving in the opposite directions with the speed of x km/hr and y km/hr.Then, the relative speed is,

**Relative speed=(x+y)km/hr**

• The ratio of the speeds of two objects is inversely proportional to the root of their time taken

**S1/S2 = root (T2/T1)**

## The ability to simplify seems to eliminate the unnecessary so that the necessary may speak.

Hans Hoffman

### Problems on Trains

**Types of Problems **

- Train crossing a man/pole/lamp post
- Train crossing a running man(Same direction)
- Train crossing a running man(Opp direction)
- Train crossing an another train/bridge/platform
- Train crossing an another running train(Same direction)
- Train crossing an another running train (Opp direction)

**Formula to calculate time taken by train to cross,**

1. A man/pole/lamp post, Time = L_{train} / S_{train}

2. A running man(Same direction), Time = L_{train} / (S_{train}-S_{man})

3. A running man(Opp direction) , Time = L_{train} / (S_{train} + S_{man})

4. An another train/bridge/platform, Time = L_{train}+L_{obj} / S_{train}

5. An another running train(Same direction, Time = L_{train} +L_{obj} / (S_{train}-S_{obj})

6. An another running train (Opp direction), Time = L_{train} +L_{obj} / (S_{train} + S_{obj})

Where,

L _{train }– Length of train

S_{train – }Speed of train

S_{man }– Speed of man

L_{obj – }Length of object/train 2

S_{obj – }Speed of object /train 2

Examples:

**A train is 600 meter long and is running at the speed of 72 km per hour. Find the time taken to cross**

*1)a man*

*2)a man running at 5 m/s in same direction*

*3)a man running at 5 m/s in opposite direction*

*4)a 200 meter long platform*

*5)a 200 meter long train running at 10 m/s in same direction*

*6)a 200 meter long train running at 10 m/s in opposite direction*

Answers:

- 30 sec 2. 40 sec 3. 24 sec 4. 40 sec 5.80 sec 6.80/3 sec

Explanation :

- 600/20 =30 sec
- 600/20-5 = 40 sec
- 600/20+5=24 sec
- 600+200/ 20 = 40 sec
- 600+200/20-10=80 sec
- 600+200/20+10= 80/3 sec

#### Example 1:

Train A travels at a speed of 90km/hr crosses a man at 8 seconds. what is the length of the train.

**Soln:**

Speed=90 km/hr

=90*(5/18)m/s

=25 m/s

Time=8 s

Length=25*8

=200 m

#### Example 2:

Chennai express of length 1050 m crosses a waiting man in 45 sec while it takes 90 sec to cross a platform.What is the length of the platform?

**Soln:**

Length of the train=1050 m

Time for man=45 s

Speed=(1050/45)m/s

Let, the length of the platform=x

(x+1050)=(1050/45)*90 (S*T=D)

x+1050=2100

x=1050

Length of the platform=1050 m