Which of the following statements about displacement in physics is false?

Introduction / Context:

This question checks conceptual understanding of displacement, a key quantity in kinematics. Displacement is a vector quantity that describes the change in position of an object in a specified direction. Distinguishing displacement from distance, and understanding its sign and units, is crucial for correctly solving motion problems in one and two dimensions.

Given Data / Assumptions:

• We are working in standard one dimensional or two dimensional motion.
• Displacement is defined as final position minus initial position, with direction.
• Distance is the total path length traveled and is always non negative.
• The question asks which statement about displacement is false.

Concept / Approach:

Displacement is a vector quantity with magnitude and direction, while distance is a scalar quantity with only magnitude. Because displacement can point in the positive or negative direction along a chosen axis, its value can be positive, negative, or zero. Displacement is always less than or equal to distance in magnitude because distance measures the full path, whereas displacement is a straight line between start and end. The SI unit of displacement is the metre, same as distance. Therefore, any statement claiming that displacement is always positive must be false.

Step-by-Step Solution:

Verification / Alternative check:

Consider a simple example of one dimensional motion along a straight line with right taken as positive. If a person walks 5 m to the right and then 3 m to the left, the displacement is +2 m, which is positive. If the person walks 3 m to the left from the origin, the displacement is -3 m, which is negative. If they walk 5 m right and then 5 m left, they return to their starting position and the displacement is zero. These examples clearly show that displacement can take positive, negative, or zero values, contradicting the claim that it is always positive.

Why Other Options Are Wrong (but true statements about displacement):

• It can be positive, negative or zero: This is a correct description of displacement as a vector quantity.
• Displacement is never greater than Distance: Distance is the length of the actual path; displacement is the shortest path between initial and final positions, so its magnitude cannot exceed distance.
• Its SI unit is metre: Both displacement and distance are measured in metres in the SI system.

Common Pitfalls:

Students sometimes treat displacement like distance and forget about direction. This leads them to think that displacement must also always be positive. Another common mistake is to confuse the terms and use them interchangeably in answers. Remember that distance answers the question "How much ground was covered?" while displacement answers "How far and in which direction is the final position from the starting point?" Keeping this difference in mind helps to avoid conceptual errors.

Final Answer:

The false statement is: It is always positive.