Motion in One Dimension (Kinematics)

Reference Frames

All measurements of position, distance, or speed must be made with respect to a reference frame. A reference frame provides a context for describing motion, including a coordinate system, an origin, a clock, and an observer.

• Coordinate system: Used to measure position, typically along an axis (e.g., x-axis).

• Origin: The starting point of measurement, often set to zero.

• Clock: Used to measure time intervals.

• Observer: The person or device making the measurement.

Example: If you are sitting on a train and someone walks down the aisle, their speed relative to the train is different from their speed relative to the ground.

Position

Position (x): The location of a particle with respect to a chosen reference point (such as the origin). Finding an object's position means determining its location relative to some reference, often the origin of a coordinate system.

• Position is measured in the SI unit of meters (m).

• Positions can be positive or negative depending on the chosen direction.

Example: If a car is at three different positions: , ,

Distance and Displacement

When an object changes its position, it moves and has both distance and displacement.

• Distance (d): The total length of the path traveled, measured along the actual path.

• Displacement (): The change in position from the starting point to the ending point, regardless of the path taken.

• Both are measured in meters (m).

Formula for Displacement:

• : initial position (m)

• : final position (m)

• : displacement (m)

Example: An object moves 70 m east of the origin and returns 30 m west. Distance traveled: Displacement:

Direction: Motion to the right: Displacement is positive. Motion to the left: Displacement is negative.

Average Velocity

Speed (s): How far an object travels in a given time interval. Velocity (v): The speed in a specific direction, including directional information.

• Average speed:

• Average velocity:

• Speed is measured in meters per second (m/s) and does not require direction.

• Velocity is measured in meters per second (m/s) and must be specified with direction.

Example 1: Runner's average velocity: , , Negative sign indicates motion to the left.

Example 2: Cyclist travels at 18 km/h for 2.5 h.

Example 3: Car travels 100 km at 50 km/h, then 100 km at 100 km/h.

Table: Common Units in Kinematics

Additional info:

• Reference frames are essential for describing motion accurately in physics.

• Displacement is a vector quantity, while distance is a scalar.

• Average velocity can be negative, zero, or positive depending on direction.

• Speed is always non-negative.