The correct option is **C. Displacement**. ### Explanation of Why Displacement is a Vector 1. **Definition of Vectors and Scalars**: - **Vectors** are quantities that have both magnitude (size) and direction. Examples include displacement, velocity, and force. - **Scalars** are quantities that have only magnitude and no direction. Examples include temperature, speed, and mass. 2. **Understanding Displacement**: - Displacement is defined as the change in position of an object. It is a vector quantity because it describes not only how far an object has moved but also in which direction it has moved. - For example, if an object moves from point A to point B, the displacement is the straight line from A to B, along with the direction of that line. If point A is at coordinates (0, 0) and point B is at (3, 4), the displacement vector can be represented as (3, 4) with a magnitude calculated using the Pythagorean theorem: \[ \text{Magnitude} = \sqrt{(3^2 + 4^2)} = \sqrt{9 + 16} = \sqrt{25} = 5. \] - The direction can be found using trigonometry, specifically the tangent function, which gives the angle of the displacement vector relative to the horizontal axis. 3. **Why the Other Options are Incorrect**: - **A. Temperature**: Temperature is a scalar quantity. It only has magnitude (e.g., 25 degrees Celsius) and does not have a direction. You cannot say "25 degrees Celsius to the north"; it simply indicates how hot or cold something is. - **B. Speed**: Speed is also a scalar quantity. It measures how fast an object is moving but does not provide any information about the direction of that movement. For example, saying a car is traveling at 60 km/h tells us the rate of travel but not the direction (north, south, etc.). - **D. Mass**: Mass is a scalar quantity that measures the amount of matter in an object. It is expressed in units such as kilograms (kg) and does not have a direction associated with it. You cannot have "5 kg to the east"; mass is simply a measure of how much matter is present. ### Summary of Key Points - **Displacement** is a vector because it has both magnitude and direction. - **Temperature**, **speed**, and **mass** are all scalar quantities, lacking direction. - Understanding the difference between vectors and scalars is crucial in physics, as it affects how we analyze and solve problems involving motion and forces. ### Revision Summary - Vectors have both magnitude and direction; scalars have only magnitude. - Displacement is a vector quantity; it indicates how far and in which direction an object has moved. - Temperature, speed, and mass are scalar quantities with no directional component. - Recognizing the type of quantity (vector vs. scalar) is essential for solving physics problems correctly.