Question

Straight distance between a hotel and a railway station is 10km, but the circular route is followed by a taxi covering $23km$ in $28\min $ . What is average speed and magnitude of average velocity? Are they equal?

Answer 1

Hint: In order to solve this question you have to know the concept of speed and velocity. You have to know the difference between speed and velocity. Also what is distance and displacement? What is the difference between distance and displacement? Also remember the formula for finding the speed and velocity.

Formula used:
The formula for a finding the average speed is given by
$s = \dfrac{d}{t}$
Where, $s$ is the average speed
$d$ is the total distance travelled
$t$ is the total time taken
The formula for finding the average velocity is given by
$v = \dfrac{d}{t}$
Where, $v$ is the average velocity
$d$ is the displacement
$t$ is the total time taken

Complete step by step solution:
It is given in the question that the total distance travelled by a taxi using the circular route is
Total distance travelled $ = 23km$
It is also given in the question that the total time taken is
Total time taken $ = 28\min $
Now convert it into hours,
$ \Rightarrow $ total time taken $ = \dfrac{{28}}{{60}}hrs$
Now apply the formula for a finding the average speed, that is given by
$s = \dfrac{d}{t}$
On putting all the values given in the question, we get
$ \Rightarrow s = \dfrac{{23}}{{\left( {\dfrac{{28}}{{60}}} \right)}}$
On solving this we get the average speed,
$ \Rightarrow s = 49.29kmph$
Now finding the average velocity
The straight distance between a hotel and a railway station is given in the question as,
Displacement $ = 10km$
Now apply the formula for finding the average velocity, that is given by
$v = \dfrac{d}{t}$
On putting all the values given in the question, we get
$ \Rightarrow v = \dfrac{{10}}{{\left( {\dfrac{{28}}{{60}}} \right)}}$
On solving this we get the average velocity,
$ \Rightarrow v = 21.43kmph$

Therefore, the two quantities that are average speed and average velocity are not equal.

Note: Keep in mind that the velocity is the vector quantity, it means it has both magnitude and direction. Also displacement is defined as the change in the position of an object, it is also a vector quantity. Always remember to change the given value in their standard unit before solving the numerical problems.