Question

A school bus takes $35\min$ to cover a distance of $14\,Km$,Calculate its speed in $Kmh{r^{ - 1}}$ and $m{s^{ - 1}}.$

Answer 1

In order to solve this question, we need to know the basic concept of speed, distance and time. Speed is the physical quantity which tells us about the rate of change of distance covered by a body with respect to time, simple speed is the ratio of distance covered by the body in a given period of time. We will use the general formula of speed to calculate its value in respective units of measurements.

Formula Used:
Speed Distance and time are related as $\text{speed} = \dfrac{\text{Distance}}{\text{time}}$
Units of measurements: $1Km = 1000m$
$1\,hour = 3600\,\sec$
$\Rightarrow 1\,hour = 60\,\min$

Complete step by step answer:
According to the question, we have given that school bus covers a distance of $14Km$ in $35\min$ or we can write
$\text{Distance} = 14\,Km$
$\Rightarrow \text{time} = 35\min$
Converting unit of time from minute in to hour using $1hour = 60\min$ so,
$35\min = \dfrac{{35}}{{60}}hour$
$\Rightarrow35\min = \dfrac{7}{{12}}hour$

Now, we have distance in Kilometres which is $Dis\tan ce = 14Km$ and time in hours which is $time = \dfrac{7}{{12}}hour$
Now using the speed formula we can find speed in Kilometre per hour.
$\text{speed} = \dfrac{\text{Distance}}{\text{time}}$
$\Rightarrow \text{speed}= \dfrac{{14 \times 12}}{7}$
$\Rightarrow \text{speed} = 24Kmh{r^{ - 1}}$
Now, in order to find this speed in units of meter per second we simply, put the values of $1Km = 1000m$ and $1hour = 3600\sec$ in the value of calculated speed which is $speed = 24Kmh{r^{ - 1}}$
$\Rightarrow \text{speed} = 24 \times (1000m) \times \dfrac{1}{{3600}}\sec$
$\Rightarrow \text{speed} = \dfrac{{20}}{3}\,m{\sec ^{ - 1}}$
$\therefore \text{speed} = 6.67\,m{\sec ^{ - 1}}$

Hence, the speed of the school bus in Kilometre per hour is $\text{speed} = 24\,Kmh{r^{ - 1}}$ and speed of school bus in meter per second is $\text{speed} = 6.67\,m{\sec ^{ - 1}}$.

Note: It should be remembered that, while solving such questions always use correct values of units of measurements and the basic difference between speed of a body and the velocity of the body is velocity is a vector quantity which has magnitude and as well as direction whereas speed is just a scalar quantity having magnitude only.