Distance

The length of the path travelled by an object or a body or a person between two places is known as distance. It is measured in meters or kilometres.
Speed :
The distance travelled by any object or person in unit time is knows as speed of the object or speed of a person. It is measured in meter per second or kilometre per hour.
Speed : Distance / Time
Distance : Speed x Time
Time : Distance / Speed
Average Speed : Total Distance Covered / Total Time Taken

Average Speed when an object travels equal distances with different speeds:

1. If a person covers two equal distances with speed of x and y units respectively, then the average speed of the man for complete journey =
2xy / x+y

2. A person travels 3 equal distances with speeds x, y and z units, then his

average speed = 3xyz / xy +yz +zx
>Conversion of Units :
1.From km/h to m/s :
To convert the speed of an object from km/h to mtr/s, multiply the speed by 5/18

S km/h = S x 5 / 18 mps

2. from mtr/s to km/h:
To convert the speed of an object from mtr/s to km/h, multiply the speed by 18 / 5

S mps= S x 18 / 5 km/h

Relation between spped and time of two object:
The ratio of the speeds of two person to cover a distance is x:y, then the ratio of time taken by them to cover same distance will be y :x.

Example1: Anumita travelled a distance of 95 kilometres in 5 hours.

So distance travelled by Anumita in 1 hour = km = 95 / 5 = 19 km

So, speed of Anumita = 19kmph

Example2: 72 km/h = 72 x 5 / 18 = 20 m/s
From m/s to km/h.

Example3: Convert 30 mtr/s into km/h

30 x18 / 5= 108 km/h

Example4: A person travels 80 km in 6 hours and next 30 km in 5 hours. What is his average speed?
Total distance covered = 80 km + 30 km = 110 km
Total time taken = 6 hours + 5 hours = 11 hours.
Average Speed =Total Distance Covered / Total Time Taken = 110 / 11 = 10 km/h

Example5. Rahul covers a half of the distance with speed of 40 km/h and remaining half of the distance with speed of 60 km/h. What is his average speed?
Answer :
He travelled two equal distance with speeds 40kmph and 60kmph
Average Speed =2 x 40 x 60 / (40+60) = 48km/h

Example 6: Avinash travels 1/3 of his journey at 10 km/h , next 1/3 at 30km/h and remaining 1/3 at 60km/h. What is his average speed during the journey? A. 15 km/h B. 20 km/h C. 25km/h D. 30km/h Answer :
Avinash travels 3 equal distances at speeds of 10 km/h, 20 km/h and 30 km/h Average Speed =3xyz/(xy + yz + zx)=3 x 10 x 30 x 60 /(10x30 + 30+60 + 60+10)= 20 km/h Concept of Relative Speed :
Objects moving in the same direction : If two objects are moving in same direction at speeds of x and y , then their relative speed = x-y
For example, if the two bikes A and B move in the same direction at speeds of 520kmph and 40 km/h , then their relative speed of A with respect to B is (50-40)=10 km/h.

Example7. Abhilash and Agniwesh start walking in the same direction at 12km/h and 10 km/h respectively. In how many hours will they be 16km apart? A. 4 hours B. 5 hours C. 6 hours D. 8 hours Answer :
Time =Distance / Speed
Here both are moving in same direction, so the relative speed is 12-10 = 2 km/h Time =16 / 2= 8 hours
Objects moving in opposite direction : If two objects are moving in opposite directions at speeds of x and y, then their relative speed = x+y.
If two cars are travelling towards each other at speeds of 30 km/h and 40 km/h respectively, then their relative speed = 30+40 = 70 km/h.

Example8. Anumita and Ruby walking in opposite directions at 12km/h and 10 km/h respectively. In how many hours will they be 66 km apart? A. 6 hours B. 33 hours C. 3 hours D. 5 hours Answer :
Anumita and Ruby are walking in opposite direction , their relative speed is sum of their speeds = 12+10 =22 km/h
Time = Distance / Time=66 / 22= 3 hours
Note : The ratio of speeds of two objects is a:b, then to cover same distance, the ratio of time taken will be b:a

Example 9: The ratio between the speeds of A and B is 5 :7 and A takes 35 minutes to cover a distance.
In what time does B covers the same distance? A. 10 min B. 15 min C. 25 min D. 30min Answer :
The ratio of between the speeds of A and B is 5:7
Then ratio of the times taken by A and B = 7:5
Time taken by A to cover a distance is 7x = 35 minutes
So, time taken by B to cover same distance = 5x = 5x5 = 25 minutes