Question

An athlete runs along a circular track of radius R what is his displacement and distance travelled by him when he cover 3/4 of the track?

Answer 1

Answer:

Displacement = R$\sqrt{2}$

Distance =  $\frac{3πR}{2}$

Explanation:

First thing first this is a mathematics question not physics.

displacement is the shortest distance between two points and the distance the length of the actual path traveled between points.

So arc ABC is the distance and chord AC is the displacement

ABC is (3/4) of the circumference and AC can be calculated by Pythagoras Theorem.

1. Displacement AC

 AC = $\sqrt{R^{2} + R^{2} }$

so AC = R$\sqrt{2}$

2. Distance ABC

 ABC = $\frac{3}{4}$ * 2 * π *R

 ABC = $\frac{3πR}{2}$