11 - University Physics with Modern Physics

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.

 

Step-by-Step Solution

Answer

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

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 case bicyclist is travelling from A to B that is a semicircle.

 

So, the distance traveled by the bicyclist will be πR.

 

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

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

 

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 displacement traveled will 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 be zero.

Therefore, displacement of bicyclist in case II is zero.