Question

A body moves over one fourth of a circular arc in a circle of radius r. Find the magnitude of distance travelled and displacement.

Answer 1

Given:

A body moves over one fourth of a circular arc in a circle of radius r.

To find:

The magnitude of distance travelled and displacement.

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)</p><p>\put(3,3){\circle{1.4}}\put(3,3){\line(1,0){0.7}}\put(3,3){\line(0,1){0.7}}\put(3,3.7){\line(1,-1){0.7}}\put(3.25,2.75){r}\put(2.75,3.25){r}\put(3.8,3){A}\put(3,3.9){B}\end{picture}}$

Calculation:

Object travels from A to B (refer to diagram).

Distance is the total path length travelled by an object.

$distance = \dfrac{1}{4} \times (2\pi r)$

$\boxed{ = > distance = \dfrac{\pi r}{2} }$

Displacement is the shortest length between starting and stopping point of the object.

$displacement = \sqrt{ {r}^{2} + {r}^{2} }$

$= > displacement = \sqrt{2 {r}^{2} }$

$\boxed{ = > displacement = r \sqrt{2} }$

Hope It Helps.