What is the angular displacement (in radians) of a person standing at the Earth's equator for 6 hours assuming the Earth has a diameter of 13750 km

π/2 radians.

Explanation:

Angular Displacement

It's the angle expressed in radians, degrees, revolutions, etc. through which a point revolves around a point called the center.

To find the angular displacement, we must recall a full revolution, or turn around the center measures 360 degrees, or 2π radians.

The Earth completes a turn every 24 hours. This means that in 6 hours, it has given 6/24 = 1/4 of a turn.

This means that, measured in radians, the angular displacement of a person during 6 hours is:

1/4*2π radians

Simplifying:

π/2 radians.

a and b sometimes have a positive value