The task for the extremum problem in robot motion is to optimize a certain objective function, such as minimizing energy consumption or maximizing speed, while satisfying constraints such as avoiding obstacles or staying within a certain workspace. This involves finding the optimal trajectory or control inputs for the robot to achieve the desired goal. The extremum problem aims to find the best solution that maximizes or minimizes the objective function under the given constraints, leading to efficient and effective robot motion planning. **

The extremum problem in robot motion involves finding the optimal path or trajectory for a robot to move from one point to another while minimizing or maximizing a certain criterion. This criterion could be the shortest distance, fastest time, least energy consumption, or any other objective function. The task description typically includes defining the start and end points, specifying any constraints such as obstacles or limitations on the robot's motion, and formulating the objective function to be optimized. The goal is to find the path or trajectory that best satisfies the given criteria while adhering to the specified constraints. **

Uniform circular motion is considered an accelerated motion because the direction of the velocity vector is constantly changing, even though the magnitude of the velocity may remain constant. This change in direction results in an acceleration towards the center of the circle, known as centripetal acceleration. This acceleration is necessary to keep an object moving in a circular path, and it is what distinguishes uniform circular motion from linear motion. Therefore, even though the speed may be constant, the change in direction of the velocity vector results in an acceleration, making uniform circular motion an accelerated motion. **

A circular motion is a uniformly accelerated motion. This is because the velocity of an object in circular motion is constantly changing as it moves around the circle, due to the change in direction of its velocity vector. This change in velocity indicates that the motion is not uniform, but rather uniformly accelerated. The acceleration in circular motion is directed towards the center of the circle and is called centripetal acceleration. **

In horizontal projectile motion, the vertical motion occurs due to the force of gravity acting on the object. While the object is moving horizontally, it is also being pulled downward by the force of gravity, causing it to follow a curved path. As a result, the object's vertical position changes over time, even though its horizontal velocity remains constant. This combination of horizontal and vertical motion results in the characteristic parabolic trajectory of a projectile. **

No, Wii Play Motion requires the use of the Wii MotionPlus accessory in order to play. The game utilizes the enhanced motion-sensing capabilities of the MotionPlus remote to accurately track player movements and gestures. Without the MotionPlus accessory, the game may not function properly or be playable. **

Uniformly accelerated motion is when an object's velocity changes at a constant rate over time, resulting in a change in speed or direction. On the other hand, uniform motion is when an object travels in a straight line at a constant speed without any changes in velocity. In uniformly accelerated motion, the object's acceleration remains constant, while in uniform motion, the object's velocity remains constant. **

In the given scenario, the uniform motion refers to the car traveling at a constant speed of 60 km/h for 2 hours. This means the car is moving at a constant velocity without any change in speed or direction. The uniformly accelerated motion occurs when the car increases its speed from 60 km/h to 90 km/h in 10 seconds. This represents a constant acceleration, as the car's velocity is changing at a uniform rate over time. **