2.1 Displacement - College Physics 2e | OpenStax

Learning Objectives

• Define position, displacement, distance, and distance traveled.
• Explain the relationship between position and displacement.
• Distinguish between displacement and distance traveled.
• Calculate displacement and distance given initial position, final position, and the path between the two.

Key Concepts

Position

• Definition: Position describes where an object is at any particular time, relative to a convenient reference frame.
• Examples:
  • A rocket's position relative to Earth.
  • A professor's position relative to a nearby whiteboard.
• Reference Frames:
  • Often, Earth is used as a reference frame for describing position.
  • For a person in an airplane, the airplane itself can be the reference frame.

Displacement

• Definition: Displacement is the change in position of an object.
• Equation:
  • ( \Delta x = x_f - x_0 )
  • Where ( \Delta x ) is displacement, ( x_f ) is final position, and ( x_0 ) is initial position.
• SI Unit: Meter (m), but other units like kilometers or miles can be used.
• Directionality: Displacement includes both magnitude and direction (positive or negative).
  • Example: Professor moves +2.0 m to the right.
  • Example: Passenger moves -4.0 m toward the rear of a plane.

Distance

• Definition: Distance is the magnitude or size of displacement between two positions.
• Distance Traveled vs. Displacement:
  • Distance traveled is the total length of the path taken.
  • Displacement considers only the difference between initial and final positions, regardless of the path.

Misconception Alert

• Distance Traveled vs. Magnitude of Displacement:
  • Distance traveled can be greater than the magnitude of displacement.
  • Example: A professor could walk 150 m during a lecture but only be displaced by +2.0 m.

Example Problem

• Scenario: Cyclist rides 3 km west, then 2 km east.
  • Displacement: ( \Delta x = -1 ) km.
  • Distance: 5 km.
  • Magnitude of Displacement: 1 km.

Conclusion

• Understanding displacement involves recognizing both the magnitude and direction of an object's change in position.
• Displacement is distinct from distance traveled, which accounts for the total path length.
• These concepts are foundational in kinematics and critical for solving physics problems involving motion.