Rectangular Coordinates

📐 Motion in a Plane Using the Rectangular Coordinate System

1. Introduction

The rectangular (Cartesian) coordinate system describes the position of a particle using its coordinates along mutually perpendicular x, y, and z axes. Since the coordinate axes are fixed in space, the associated unit vectors remain constant throughout the motion. This makes the Cartesian coordinate system the simplest and most commonly used framework for describing particle kinematics.

2. Animation Details

Coordinate System: Rectangular (Cartesian) (x, y, z)

Animation: Planar motion in the x–y plane

Trajectory: x(t) = t, y(t) = 3 - 0.25(t - 2.5)², z(t) = 0

Vectors Displayed: Position, Velocity, Acceleration

Learning Objective: Visualize particle kinematics in a fixed Cartesian coordinate system.

3. Kinematic Equations

4. Key Observations

• The coordinate axes and unit vectors remain fixed throughout the motion.

• The velocity vector is always tangent to the trajectory.

• The acceleration vector is independent of the coordinate system orientation.

• The unit vectors i, j, and k form a fixed right-handed orthogonal coordinate system.

5. Watch For

• Observe that the x and y axes remain fixed throughout the animation.

• Notice that the position, velocity, and acceleration vectors are resolved along the same fixed directions.

• Observe that the acceleration vector remains vertically downward during the entire motion.