Which of the following best describes the difference between $\mathrm{speed}$ and $\mathrm{acceleration}$?

• A. $\mathrm{Speed}$ is the rate at which an object's $\mathrm{acceleration}$ changes, while $\mathrm{acceleration}$ is the rate at which an object covers distance.
• B. $\mathrm{Speed}$ is the rate at which an object covers distance, while $\mathrm{acceleration}$ is the rate at which an object's $\mathrm{velocity}$ changes over time.
• C. $\mathrm{Speed}$ is a vector quantity, while $\mathrm{acceleration}$ is a scalar quantity.
• D. $\mathrm{Speed}$ and $\mathrm{acceleration}$ both measure how fast an object moves, but $\mathrm{acceleration}$ is always greater than $\mathrm{speed}$.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definition of speed. Speed is a scalar quantity that measures how fast an object covers distance, regardless of direction. It is given by the formula \(\text{speed} = \frac{\text{distance}}{\text{time}}\).
2. Step 2: Understand the definition of acceleration. Acceleration is a vector quantity that measures the rate of change of velocity with respect to time. It can be expressed as \(\mathbf{a} = \frac{\Delta \mathbf{v}}{\Delta t}\), where \(\Delta \mathbf{v}\) is the change in velocity and \(\Delta t\) is the change in time.
3. Step 3: Recognize the difference between speed and acceleration. Speed tells you how fast an object is moving, while acceleration tells you how the velocity (which includes both speed and direction) is changing over time.
4. Step 4: Note that speed is scalar (only magnitude) and acceleration is vector (magnitude and direction). This means acceleration can change the speed, the direction of motion, or both.
5. Step 5: Conclude that the correct description is: Speed is the rate at which an object covers distance, while acceleration is the rate at which an object's velocity changes over time.