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# In one second a particle goes from point A to point B moving in a semicircle find the magnitude of average velocityA. $1\,m/s$B. $2\,m/s$C.$0.5\,m/s$D. none of these

Last updated date: 20th Jun 2024
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Hint- Average velocity is the ratio of displacement by the time taken.
It is given by the equation
${V_{avg}} = \dfrac{d}{t}$
Where $d$ is the displacement and $t$ is the time taken.
Displacement is the shortest distance between the initial and final positions
Using this we can find the answer to this question.

Step by step solution:
Average velocity is the ratio of displacement by the time taken.
It is given by the equation
${V_{avg}} = \dfrac{d}{t}$
Where $d$ is the displacement and $t$ is the time taken.
From the figure we can see that the radius of the semicircle is
$r = 1\,m$
In order to calculate average velocity we need to find the displacement of the particle. Displacement is the shortest distance between the initial and final positions. Here, the shortest path between A and B is that diameter of the semicircle.
We know that diameter is twice the radius
$d = 2r$
Therefore, displacement is
$d = 2 \times 1\,m = 2\,m$
We are asked to find the average velocity in one second. Thus, time taken
$t = 1\,s$
Substitute the value of displacement and time taken in the equation for average velocity.
${V_{avg}} = \dfrac{d}{t}$
$\Rightarrow {V_{avg}} = \dfrac{{2\,m}}{{1\,s}}$
$\therefore {V_{avg}} = 2\,m/s$
Therefore, the magnitude of average velocity is $2\,m/s$

Hence the answer is option B

Note:While calculating the displacement always remember that displacement is the shortest path between the initial and final positions whereas distance is the actual path travelled by the particle. Here the distance will be half of the circumference of the circle that is,$\pi r$ . This should not be taken as the displacement. The shortest distance the particle travels is along the diameter. From the figure we can see that AB is the diameter of the semicircle.so we can calculate this value by taking twice the value of radius.