Problem Statement:
In a rigid body in plane motion, the point That is accelerating with respect to point People at 10 180 m/s². If the instantaneous acceleration of point Q is zero, the acceleration (in m/s²) of point R is?

Solution:

Understanding Rigid Body in Plane Motion:
A rigid body in plane motion is a system of particles in which the distance between the particles remains constant throughout the motion. The motion of a rigid body can be described by the motion of a single point on the body, known as the center of mass. The motion of a rigid body can be divided into two types of motion: translational motion and rotational motion.

Translational Motion:
Translational motion is the motion of a rigid body in which every point on the body moves in a straight line with the same velocity. The acceleration of a point on a rigid body is the sum of the translational acceleration and the rotational acceleration.

Rotational Motion:
Rotational motion is the motion of a rigid body in which every point on the body moves in a circle around a fixed axis. The rotational acceleration of a point on a rigid body is the product of the radius of the circle and the angular acceleration.

Acceleration of Point That:
Given, the point That is accelerating with respect to point People at 10 180 m/s².
This means the acceleration of point That is 10 180 m/s² relative to point People.

Acceleration of Point Q:
The instantaneous acceleration of point Q is zero.
This means, the velocity of point Q is constant.

Acceleration of Point R:
As the rigid body is in plane motion, the acceleration of point R can be divided into two components: translational acceleration and rotational acceleration.

Translational Acceleration:
The translational acceleration of point R is the same as the translational acceleration of point That, which is 10 180 m/s².

Rotational Acceleration:
The rotational acceleration of point R is the product of the radius of the circle and the angular acceleration.
As the instantaneous acceleration of point Q is zero, it means the point Q is moving in a circle with a constant speed. Therefore, the angular acceleration of point Q is also zero.
As the rigid body is in plane motion, all the points on the body move in a circle around a fixed axis. Therefore, the radius of the circle is the same for all the points on the body.
Hence, the rotational acceleration of point R is also zero.

Conclusion:
The acceleration of point R is the sum of the translational acceleration and the rotational acceleration. As the translational acceleration of point R is 10 180 m/s² and the rotational acceleration is zero, the total acceleration of point R is 10 180 m/s².