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It takes you $9.5\min $ to walk with an average velocity of $1.2m{s^ - }^1$ to the north from the bus stop to museum entrance. What is your displacement? $\left( {i{n^{}}m} \right)$
(A) $684$
(B) $540$
(C) $525$
(D) $565$

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Last updated date: 13th Jun 2024
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Answer
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Hint Displacement can be calculated by multiplying the velocity of the person with the time for which he/she has traveled. While multiplying, take care of the units of time and velocity. In this problem, the unit of time is minutes while the unit of velocity is $m/s$. Convert the time to seconds or velocity to $m/\min $ get the correct answer.

Formula Used:
We know that,
Average velocity $= \dfrac{{Total \, displacement}}{{Total \, time \, taken}}$
Or, $v = \dfrac{s}{t}$
Where, $v$ is the average velocity,
$s$ is the displacement,
And, $t$ is the time taken.

Complete step by step answer:
We know that,
$v = \dfrac{s}{t}$
We can modify this equation for this problem like
$s = vt$ $ - - - - (1)$
Now, we convert the units of time from minutes to seconds.
$t = 9.5\min $
Or, $t = 9.5 \times 60$
That gives us,
$ \Rightarrow t = 570s$
Using the equation$(1)$, we get
$s = 1.2 \times 570$
$ \Rightarrow s = 684m$

Thus, Option (A) is correct.

Additional Information You should know that there is a difference between distance and displacement. The person can move $100m$ from the starting point and come back. In this case, displacement will be zero, but the distance traveled by the cyclist will be $2 \times 100 = 200m$. The same thing can be said about speed and velocity. Speed is the distance traveled over a given time while velocity is displacement over time. Distance and speed are scalars while displacement and velocity are vectors. Importantly, always try to check the units before calculating numerically.

Note You can observe that the direction of the motion has been given. But since the person never changes direction, it is not important to notice the direction in this problem. However, if a person changes direction, you need to calculate the straight line distance from the starting point to the endpoint to get the proper displacement.