Question

A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain.

Short answer

Displacement of bicyclist in case I is 1000 m and case II is zero.

Step-by-step solution

Given Data: 

The radius of racetrack is r=500 m.

Displacement 

In Simple words displacement is the shortest distance travelled by an object.

Here in first casebicyclistis travelling from A to B that is a semicircle.

So, the distance traveled by thebicyclistwill be πR.

Now the displacementtraveledis the minimum distance between point A and B that is diameter AB.

$$\begin{gathered} Displacement=AB \\ =2R \\ =2\left(500m\right) \\ =1000m \end{gathered}$$

Thus, the displacement is 1000 m.

Displacement in Case II

When the body is completing one full rotation the distance traveled by the body is 2πR.

The displacementtraveledwill be the minimium distance between point A and B.

As it completes one circle the point A and B will be same .

So, the displacement between the points will bezero.

Therefore, displacement of bicyclist in case II is zero.