Question

Nisha swims in a $90m$ long pool. She covers $180m$ in one minute by swimming from one end to the other and back along the straight path. Find the average velocity of Nisha.
A) $0m/s$
B) $3m/s$
C) $6m/s$
D) $\text{None of these}$

Answer 1

Hint: Displacement can be defined as the shortest distance travelled between two points. When we divide this total displacement by the total time taken to cover that distance, we obtain velocity of the body that is in motion.

Formula used:
$v = \dfrac{d}{t}$

Complete step by step solution:
Displacement, as defined above, is a vector quantity and it has both magnitude and direction.
Since in the above question, we need to find the velocity of Nisha, we consider displacement made by her.
We know,
$v = \dfrac{d}{t}$
where,
$v = $ Velocity
$d = $ Distance travelled
$t = $ Time taken
Now the direction of Nisha when she goes from one end of the pool to the other is opposite to the one when she comes back taking the same path.
In the case of vector quantities, we consider a negative sign to denote the opposite direction.
Therefore, if the distance covered by Nisha when she goes from one end to other $ = 90m$
Then, the distance covered by her when she returns in the same path is $ = - 90m$
Therefore, displacement made by her,
$\Rightarrow d = 90m + ( - 90m) = 0m$
Also, displacement of an object that goes in a path and returns through the same path is zero.
Now, we know,
$v = \dfrac{d}{t}$
Time taken by Nisha,
$\Rightarrow t = 1\min = 60\sec $
Thus, we obtain:
Velocity, $v = \dfrac{0}{{60}}$
Thus, Velocity, $v = 0m/s$
Since velocity is zero; average velocity is also zero.

Therefore, we get the correct option to be (A).

Note: Distance and displacement are often confused. It should be kept in mind that distance is a scalar quantity having only magnitude. It refers to the maximum space between two points. On the other hand, displacement is a vector quantity and it refers to the shortest path taken by an object.