Distance and Displacement Calculation for an Athlete on a Circular Track

To calculate the distance and displacement of an athlete running on a circular track, we can follow these steps:

Step 1: Understand the Given Information
We are given that the athlete runs on a circular track with a radius of 50 meters. The athlete starts at point A and takes 50 seconds to reach point B, which is at the other end of the diameter drawn from A.

Step 2: Define Distance and Displacement
Distance is the total length covered by the athlete during the entire journey, whereas displacement is the shortest straight-line distance between the starting and ending points, along with the direction.

Step 3: Calculate Distance
Since the athlete runs on a circular track, the distance covered can be calculated using the formula:
Distance = Circumference of the Circle

The circumference of a circle is given by the formula:
Circumference = 2πr

Substituting the given radius value of 50 meters into the formula, we get:
Circumference = 2 * π * 50
Distance = 100π meters

Hence, the distance covered by the athlete is 100π meters.

Step 4: Calculate Displacement
To calculate the displacement, we need to find the shortest distance between the starting point A and the ending point B, along with the direction. In this case, point B is at the other end of the diameter drawn from point A.

As the athlete runs along the circular track, the diameter acts as a straight-line path connecting the two points. Therefore, the displacement is equal to the length of the diameter, which is twice the radius.

Displacement = 2 * 50
Displacement = 100 meters

Hence, the displacement of the athlete is 100 meters.

Summary:
- The distance covered by the athlete on the circular track is 100π meters.
- The displacement of the athlete is 100 meters, which is the shortest straight-line distance between the starting and ending points.

It's important to note that distance is a scalar quantity as it only considers the magnitude, while displacement is a vector quantity as it considers both magnitude and direction. In this case, since the athlete runs in a circular path, the displacement is equal to the diameter of the circular track.