The correct option is **C**: Speed is a scalar quantity that only considers magnitude, while velocity is a vector quantity that includes both magnitude and direction. ### Detailed Explanation: 1. **Understanding Speed and Velocity**: - **Speed** is defined as the distance traveled per unit of time. It is a measure of how fast an object is moving, but it does not provide any information about the direction of that movement. Because it only has magnitude (how much), speed is classified as a **scalar quantity**. - **Velocity**, on the other hand, is defined as the rate of change of displacement (which is the change in position) per unit of time. Displacement is a vector quantity that considers both the distance and the direction of the movement. Therefore, velocity includes both magnitude (how fast) and direction (where to), making it a **vector quantity**. 2. **Why Option C is Correct**: - Option C correctly states that speed is a scalar quantity (only magnitude) and that velocity is a vector quantity (magnitude and direction). This distinction is fundamental in physics, as it affects how we analyze motion. For example, if a car travels 60 km/h, that is its speed. If it travels 60 km/h to the north, that is its velocity. 3. **Why the Other Options are Incorrect**: - **Option A**: "Speed is a vector quantity that includes direction, while velocity is a scalar quantity." - This statement is incorrect because it reverses the definitions of speed and velocity. Speed is not a vector; it does not include direction. Velocity is the one that includes direction. - **Option B**: "Speed is the rate of change of position, while velocity is simply the distance traveled over time." - This statement is misleading. Speed is not the rate of change of position; that definition applies to velocity. Speed is the total distance traveled divided by the time taken, without regard to direction. Velocity, however, is the rate of change of displacement, which does consider direction. - **Option D**: "Speed can be negative, while velocity is always positive." - This statement is incorrect. Speed, being a scalar, is always a non-negative quantity (it cannot be negative). Velocity can be negative if the object is moving in the opposite direction to the defined positive direction. For example, if an object moves to the left (considered negative direction), its velocity can be negative, but its speed remains positive. ### Formulas and Concepts: - **Speed (s)**: \[ s = \frac{d}{t} \] where \(d\) is distance and \(t\) is time. - **Velocity (v)**: \[ v = \frac{\Delta x}{t} \] where \(\Delta x\) is the change in position (displacement) and \(t\) is time. ### Common Pitfalls: - Confusing speed with velocity due to their similar contexts in motion problems. - Forgetting that speed does not have a direction, which can lead to errors in vector addition or subtraction when analyzing motion. - Misunderstanding that speed cannot be negative, while velocity can be, depending on the chosen reference direction. ### Revision Summary: - Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). - Speed measures how fast an object is moving, while velocity measures how fast and in what direction. - Speed cannot be negative; velocity can be negative depending on the direction of motion. - Always remember the definitions and the formulas for both speed and velocity to avoid confusion in problems related to motion.