Question

A bus is at a speed of 108 kmph. How much does it cover in 20 seconds?

Answer 1

Hint:
The term speed is seen as the rate of change of position of an object with respect to time and is defined as the ratio of distance covered to unit time. The formula of speed is:
Speed (S) = $\dfrac{{{\text{Distance (D)}}}}{{{\text{Time (T)}}}}$
The SI unit of speed is expressed as the combination of the basic unit of distance and time. The SI unit of speed is meter per second (or usually written as m/s). But in everyday life, kilometre per hour is used as the unit of speed as it is more comfortable when expressing for road travels etc.
Speed is defined as a measure of how quickly an object moves from one place to another place. It is equal to the distance travelled divided by the time taken. It is possible to find any of these three values using the other two variables available.
\[
  time = \dfrac{{dis\tan ce}}{{Speed}} \\
  dis\tan ce = speed \times time \\
 \]

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}{\text{ }}$$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 already know that, 1 km = 1000 m and 1 hr = 3600 s
Hence, we convert the value of speed from kilometre per hour to meter per second and will get:
Speed = $108{\text{ }}\dfrac{{km}}{{hr}}{\text{ = 108}}\left( {\dfrac{{1000m}}{{3600s}}} \right) = 30\dfrac{m}{s}$
$Speed = 30\dfrac{m}{s}$
So, the speed of the train expressed in meters per second is 30 m/s.
Now Speed = 30 m/s
Time = 20 sec
So, Distance = $Speed \times Time = 30 \times 20 = 600m$

Therefore, a bus at a speed of 108 kmph covers 600 m in 20 seconds.

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, distance, and time problems usually are asking you to solve for one of the three variables given certain information about the other two variables.