At what temperature will the speed of sound in air be 1.75 times it's speed at NTP?Justify
Answers
Explanation:
Speed of a body is the distance covered by the body in unit time.
Therefore Speed=
\dfrac{Distance}{Time} which implies:
Distance = Speed \times Time
Time = \dfrac{Distance}{Speed}
1. In order to find speed, if :
Distance is in metre (m) and time in second (s); then the speed is in metre per second (m/s)
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:
Speed is in metre per second (m/s); time must be in second .
Speed is in Kilometer per hour (Km/h);time must be in hour
3. In order to find time, if:
Speed is in Kilometer per hour (Km/h), distance must be in Kilometer.
Speed is in metre per second(m/s), distance must be in metre.
Unit of Speed
\because
Speed=\dfrac{Distance}{Time}
\therefore
unit \: of \: speed=\dfrac{unit \: of \: distance}{unit \: of \: time}
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
\dfrac{distance \: covered}{time \: taken}=\dfrac{8 \: cm}{4 \: sec}=2 \: cm/s
So here,
unit \: of \: speed=\dfrac{cm}{sec}=cm/s
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
\dfrac{5}{18} .
To convert m/s into Km/h, we multiply by
\dfrac{18}{5} .
Reason:
1 \: Km/h= \dfrac{1 \: Kilometre}{1 \: hour}= \dfrac{1000 \: metre}{60 \times 60 \: second} = \dfrac{5}{18} \: m/s
Example: Convert:
90 Km/h into m/s
15 m/s into Km/h
75 cm/s into Km/h
45 Km/h into m/min
Solution:
1.
90 \: Km/hr =(90 \times \dfrac{5}{18}) \: m/s= 25 \: m/s
2.
15 \: m/s =(15 \times \dfrac{18}{5}) \: Km/h = 54 \: Km/h
3.
75 \: cm/s =0.75 \: m/s (
\because
75 cm=\dfrac{75}{100} \: m =0.75 \: m )
=(0.75 \times \dfrac{18}{5}) \: m/s =2.7 \: Km/h
4.
45 \: Km/h =\dfrac{45 \: Km}{1 \: hr}= \dfrac{(45 \times 1000) \: m}{60 \:min}=750 \: m/min
Example: A boy covers a distance of 1.2 km in 40minutes. Find his speed in:
Kilometre per hour (Km/h)
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 =
\dfrac{40}{60} \: hr =\dfrac{2}{3} \: hr
\therefore
Speed =\dfrac{Distance}{Time} =1.2 Km \div \dfrac{2}{3} \: hr=(1.2 \times \dfrac{3}{2}) \: Km/h=1.8 \: Km/h
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:
Distance =1.2 Km =(1.2 \times 1000) \: m=1200 \: m
and,
Time=40 \: min=(40 \times 60) \: sec=2400 \: sec
$latex\ therefore $
Speed = \dfrac{Distance}{Time}= \dfrac{1200 \: m}{2400 \: sec}=\dfrac{1}{2} \: m/s =0.5 \: m/s
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:
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.
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.
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:
His speed
The distance run by him in 5 seconds
The time taken by him to cover
\dfrac{2}{5} Km
Solution:
1.
Speed= \dfrac{Distance}{Time}=\dfrac{200}{25} \: m/sec= 8 \: m/s
2. Distance run in 5 sec
= Speed \times Time = 8m/s \times 5 \: sec=40 \: m
3. Time taken to cover
\dfrac{2}{5} \: Km
=\dfrac{Distance}{Speed}= \dfrac{400 \: m}{8 \: m/s}=50 \: sec
[
\because
\dfrac{2}{5} Km= (\dfrac{2}{5} \times 1000) \: m=400 \: m]
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=
\dfrac{total \: distance \: covered}{total \: time \: taken}
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 =
\dfrac{420 Km}{7 hr} = 60 \: Km/h
Example: A man covers first 60 Km of his journey at 30 Km/h and remaining 50 Km at 20 Km/h. Find:
The total time taken
His average speed during the whole journey
Solution :
1. Time taken to cover first
60 Km = \dfrac {60}{30} \: hr = 2 \: hr
(
\because
Time=\dfrac {Distance}{Speed} )
and, time taken to cover remaining
50 \: Km= \dfrac{50}{20} hr= \dfrac{5}{2} \: hr
\therefore total time taken
= 2 \: hr + \dfrac{5}{2} \: hr = \dfrac{9}{2} hr
2. Since , total distance covered= 60 Km + 50 Km =110 Km
and total time taken