Question

A bus moves with an average speed of 60 kilometers per hour for 4.5 hours. Find the distance traveled by it.

Answer 1

Hint: Average speed is the ratio of total distance to the total time taken. It is given by the equation
${v_{avg}} = \dfrac{x}{t}$
Where, $x$ is the total distance and $t$ is the time taken
Using this equation we can find the total distance travelled.

Complete step by step answer:
Given,
The average speed of the bus, ${v_{avg}}$ is $60\,km/hr$.
$1\,km$ is $1000\,m$.
$1\,hr$ is $60\,\min $.
$1\min $ is $60\,s$.
$\therefore 1\,hr = 60 \times 60\,s = 3600\,s$
So, in order to convert $60\, km/hr$ into $m/s$ we need to multiply the numerator by 1000 and denominator by 3600.
That is,
${v_{avg}} = \dfrac{{60\,km}}{{1\,hr}} = \dfrac{{60\, \times 1000}}{{1 \times 3600}} = 16.66\,m/s$
Time taken is given as $45\,hr$. Thus,
$t = 45\,hr = 45 \times 3600\,s = 16200\,s$
We need to find the distance travelled by the bus.
Average speed is the ratio of total distance to the total time taken. It is given by the equation
${v_{avg}} = \dfrac{x}{t}$
Where $x$ is the total distance and $t$ is the time taken
From this we can calculate the distance as
$x = {v_{avg}} \times t$
Substitute the given values then we get
$\Rightarrow x = 16.666 \times 16200 $
$\Rightarrow x = 269892\,m $
$\Rightarrow x = 269.8\,km $
$x \approx 270\,km $

Therefore, the distance traveled by bus is 270km.

Note:
Speed is a scalar quantity. It has only magnitude. This is because the distance is a scalar quantity. Distance is the length of the path traveled. Hence it does not have a direction.
Whereas the average velocity calculated using displacement is a vector quantity. Displacement is the shortest path traveled. It has both magnitude and direction.