Q.6: If a man is running at a speed of 32km/hr for 3 hour 20 minutes. Find the distance he covered.
Answers
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