Question

An object travels around a circle of radius $6m$ with speed $3\pi m{s}^{-1}$. Find the distance and displacement after $3s$.

• A. $9\pi m,6\sqrt{2}m$
• B. $9\pi m,0m$
• C. $12\pi m,6\sqrt{2}m$
• D. $12\pi m,0m$

Answer 1

The correct option is A $9\pi m,6\sqrt{2}m$

Given:
Radius of the circle, $r=6m$
Time taken, $t=3s$
Speed, $v=3\pi m{s}^{-1}$
Distance travelled is the product of speed and time.
$d=3\pi \times 3=9\pi m$
Circumference, $C=2\pi r=12\pi m$
In 3s it would have travelled,
$d_3=\frac{9\pi }{12\pi }={\left(\frac{3}{4}\right)}^{th}$ of the circle.
We know, displacement is the shortest distance between initial and final points.
Since the object covers ${\left(\frac{3}{4}\right)}^{th}$ of the circle), the object starts its journey from point A and ends its journey at point B.
Therefore, displacement of the object is AB.
$AB=\sqrt{{AO}^2+{OB}^2}$
$AB=\sqrt{6^2+6^2}$ (using Pythagoras theorem)
$AB=6\sqrt{2}m$