Speed: Unit of Speed, Variable and Average Speed …

Speed of a body is the distance covered by the body in unit time.

Therefore Speed= which implies:

1. In order to find speed, if :

1. Distance is in metre (m) and time in second (s); then the speed is in metre per second (m/s)
2. Distance is in Km (Km) and time in hour (h); then the speed is in Kilometer per hour (Km/h)

2. In order to find the distance, if:

1. Speed is in metre per second (m/s); time must be in second .
2. Speed is in Kilometer per hour (Km/h);time must be in hour

3. In order to find time, if:

1. Speed is in Kilometer per hour (Km/h), distance must be in Kilometer.
2. Speed is in metre per second(m/s), distance must be in metre.

Unit of Speed

Now, the various units of distance are metre, centimetre, Kilometre etc. and the various units of time are hour, minutes and seconds.

So, say we take the unit of distance to be centimetre (cm.) and the unit of time to be second (s.).

Example: A snail covers a distance of 8 cm in 4 seconds.

So the speed of the snail is

So here,

The two most widely used units of speed are as follows: metre/sec or m/s and Kilometre/hour or Km/h.

Example: The speed of sound in air is 330 m/s.

Example: The car is travelling at a speed of 60 Km/h.

Speed Unit Conversion

To convert speed from Kilometre per hour (Km/h) into metre per second (m/s), we multiply by .

To convert m/s into Km/h, we multiply by .

Reason:

Example: Convert:

1. 90 Km/h into m/s
2. 15 m/s into Km/h
3. 75 cm/s into Km/h
4. 45 Km/h into m/min

Solution:

1.

2.

3. ( )

4.

Example: A boy covers a distance of 1.2 km in 40minutes. Find his speed in:

1. Kilometre per hour (Km/h)
2. Meter per second (m/s)

Solution:

1. In order to get speed in Kilometre per hour , the distance covered must be in Kilometre and the time taken must be in hour

Given: Distance =1.2 Km and Time =40 min =

2. In order to get speed in metre per second, the distance covered must be in metre and the time taken must be in second.

Given:

and,

$latex\ therefore $

Uniform and Variable speed

If a body covers equal distances in equal intervals of time ;it’s speed is said to be uniform otherwise it’s speed is variable.

For example:

1. If a car covers 60 Km in first hour, 60 Km in second hour, 60 Km in third hour and so on, it’s speed is uniform.
2. If a car covers 60 Km in first hour,67 Km in second hour ,58 km in third hour and so on, it’s speed is variable.
3. If a car covers first 60 Km in one hour, second 60 Km in 1 hour 20 minutes , third 60 km in 1 hour 30 minutes and so on, then also it’s speed is variable.

Example: A man runs 200 metre in 25 second. Find:

1. His speed
2. The distance run by him in 5 seconds
3. The time taken by him to cover

Solution:

1.

2. Distance run in 5 sec

3. Time taken to cover

[

Example: A train covers first 120 Km in 2 hours, next 160 Km in 3 hours and last 140 Km again in 2 hours. Find the average speed of the train.

Solution:

Average speed of an object=

Since, total distance covered =120 Km+160 Km+140 Km =420 Km

And, total time taken= 2 hrs + 3 hrs+ 2 hrs= 7 hours

Therefore average speed =

Example: A man covers first 60 Km of his journey at 30 Km/h and remaining 50 Km at 20 Km/h. Find:

1. The total time taken
2. His average speed during the whole journey

Solution :

1. Time taken to cover first

( )

and, time taken to cover remaining

total time taken

2. Since , total distance covered= 60 Km + 50 Km =110 Km

and total time taken

average speed

Note: When a train passes:

1. A pole or any other stationary object, the minimum distance covered by the train= length of the train.
2. A platform, the minimum distance covered by the train= length of the train + length of the platform.

Example: A 160 m long train is travelling at a speed of 72 Km/h, find the time taken by the train to pass:

1. A telegraph post
2. A 200 m long platform.

Solution:

1. Distance to be covered= length of the train=160m

Speed

2. Distance covered=length of the train +length of the platform=160 m + 200 m =360 m

Exercise

1. Fill in the blanks :
   1. A distance of 1.4 Km is covered in 10 min , then speed=_______Km/min
   2. A distance of 32 Km is covered in 1.6 hrs , then speed=________Km/min
   3. A car moves at 60 Km/h for 40 min , then distance covered =_________Km
   4. Speed = 15 km/min and time =1 hr ,then distance covered =________ Km
   5. If speed =18 m/sec and distance covered =2.7 Km ; time taken =__________sec=_________min
2. A train covers 51 Km in 3 hours. Calculate it’s speed. How far does the train go in 30 minutes?
3. A motorist travelled the distance between two towns , which is 65 Km, in 2 hours and 10 minutes. Find his speed in metre per minute.
4. A train travels 700 metres in 35 seconds. What is it’s speed in Km/h?
5. A racing car covered 600Km in 3 hours 20 minutes. Find it’s speed in metre per second. How much distance will the car cover in 50 sec?
6. Rohit goes 350 Km in 5 hours. Find:
   1. His speed
   2. The distance covered by Rohit in 6.2 hours
   3. The time taken by him to cover 210 Km. (Assume that throughout the journey , the speed of Rohit remains uniform).
7. A boy drives his scooter with a uniform speed of 45 Km/h. Find:
   1. The distance covered by him in 1 hour 20 min.
   2. The time taken by him to cover 108 Km.
   3. The time taken to cover 900 m.
8. I travel a distance of 10 Km  and come back in 2.5 hours . What is my speed?
9. A man walks a distance of 5 Km in 2 hours. Then he goes in a bus to the nearby town , which is 40 Km, in further 2 hours. From there, he goes to the office in an autorickshaw, a distance of 5 Km in 0.5 hour. What was his average speed during the whole journey?
10. Jagan went to another town such that he covered 240Km by a car going at 60 Km/h. Then he covered 80 Km by a train , going at 100 Km/h, and the rest 200 Km, he covered by a bus, going at 50 Km/h . What was his average speed during the whole journey?
11. The speed of sound in air is about 330 m/s. Express this speed in Km/h. How long will the sound take to travel 99 Km?
12. Convert :
    1. 54 Km/h into m/s
    2. 2.5 m/s into Km/h
    3. 16.2 Km/h into m/s
    4. 9 m/s into Km/h
    5. 8 Km/min into Km/h
    6. 8 Km/min into m/s
    7. 75 cm/s into m/s and then Km/h
    8. 120 cm/min into m/s and then Km/h
    9. 7.2 Km/h into m/s and then m/min
13. A train 180 m long is running at a speed of 90 Km/h . How long will it take to pass a railway signal?
14. A train whose length is 150 m , passes a telegraph pole in 10 sec . Find the speed of the train in Km/h.
15. A train 120 m long passes a railway platform 160 m long in 14 sec . How long will it take to pass another platform which is 100 m long?
16. Mr. Amit can walk 8 Km in 1 hour 20 minutes.
    1. How far does he go in:
       1. 10 minutes
       2. 30 seconds
    2. How long will it take him to walk:
       1. 2500 m
       2. 6.5 Km
17. Which is greater: a speed of 45 Km/h or a speed of 12.25 m/sec? How much is the distance travelled by each in 2 seconds?
18. A and B start from the same point and at the same time with speeds 15 Km/h and 12 Km/h respectively . Find the distance between A and B after 6 hours if both move in: i)same direction ii) opposite directions .
    1. Hint: required distance =Difference between the distances covered by A and B
    2. Hint: required distance = Sum of the distances covered by A and B).
19. A and B start from the same place, in the same direction and at the same time with speeds 6 Km/h and 2 m/sec respectively. After 5 hours who will be ahead and by how much?