A train moves with a speed of 108 km/hr. Its speed in meters per second is:
A.10.8
B.18
C.30
D.38.8
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Hint: The term speed generally refers to the rate of change of position of an object in any direction and is defined as the ratio of distance covered to unit time. The formula of speed is given by:
Speed (S) = $\dfrac{{{\text{Distance (D)}}}}{{{\text{Time (T)}}}}$
The SI unit of speed is given as the combination of the basic unit of distance and the basic unit of time. The SI unit of speed is meter per second. But in everyday life, kilometre per hour is used as the unit of speed.
Complete step by step solution:
Units Conversion: Conversion of units is important here
$
1\dfrac{{km}}{h}=\dfrac{{1km}}{h} \times \dfrac{{1000m}}{{1km}} \times \dfrac{{1hr}}{{3600s}} = \dfrac{{1000m}}{{3600s}} = \dfrac{5}{{18}}\dfrac{m}{s} \\
1\dfrac{m}{s} = \dfrac{{1m}}{s} \times \dfrac{{1km}}{{1000m}} \times \dfrac{{3600s}}{{1hr}} = \dfrac{{3600km}}{{1000hr}} = \dfrac{{18}}{5}\dfrac{{km}}{h} \\
$
According to the question,
Speed = 108 km/hr
We know that,
1 km = 1000 m
1 hr = 3600 s
Therefore, to convert speed from kilometre per hour to meter per second
Speed = $108{\text{ }}\dfrac{{km}}{{hr}}{\text{ = 108}}\left( {\dfrac{{1000m}}{{3600s}}} \right) = 30\dfrac{m}{s}$
Speed = $30\dfrac{m}{s}$
Hence, the speed of the train in meters per second is 30 m/s.
∴ Option (C) is correct.
Note: To convert speed given in km/hr into m/sec directly, we multiply the speed by $\dfrac{5}{{18}}$ and to convert speed given in m/sec into km/hr we have to multiply the speed it by $\dfrac{{18}}{5}$.
Speed (S) = $\dfrac{{{\text{Distance (D)}}}}{{{\text{Time (T)}}}}$
The SI unit of speed is given as the combination of the basic unit of distance and the basic unit of time. The SI unit of speed is meter per second. But in everyday life, kilometre per hour is used as the unit of speed.
Complete step by step solution:
Units Conversion: Conversion of units is important here
$
1\dfrac{{km}}{h}=\dfrac{{1km}}{h} \times \dfrac{{1000m}}{{1km}} \times \dfrac{{1hr}}{{3600s}} = \dfrac{{1000m}}{{3600s}} = \dfrac{5}{{18}}\dfrac{m}{s} \\
1\dfrac{m}{s} = \dfrac{{1m}}{s} \times \dfrac{{1km}}{{1000m}} \times \dfrac{{3600s}}{{1hr}} = \dfrac{{3600km}}{{1000hr}} = \dfrac{{18}}{5}\dfrac{{km}}{h} \\
$
According to the question,
Speed = 108 km/hr
We know that,
1 km = 1000 m
1 hr = 3600 s
Therefore, to convert speed from kilometre per hour to meter per second
Speed = $108{\text{ }}\dfrac{{km}}{{hr}}{\text{ = 108}}\left( {\dfrac{{1000m}}{{3600s}}} \right) = 30\dfrac{m}{s}$
Speed = $30\dfrac{m}{s}$
Hence, the speed of the train in meters per second is 30 m/s.
∴ Option (C) is correct.
Note: To convert speed given in km/hr into m/sec directly, we multiply the speed by $\dfrac{5}{{18}}$ and to convert speed given in m/sec into km/hr we have to multiply the speed it by $\dfrac{{18}}{5}$.