Vectors vs. Scalars in Physics

Steps:

• Recall that vectors have both magnitude and direction, while scalars have only magnitude.
• Classify each option: distance (scalar, total path length), speed (scalar, rate of motion), acceleration (vector, rate of velocity change), time (scalar, duration).
• Identify the one with direction: acceleration depends on velocity's change in magnitude or direction.
• Confirm via definition: acceleration $\vec{a} = \frac{\Delta \vec{v}}{\Delta t}$, where is vector velocity.

Why C is correct:

• Acceleration is a vector per Newton's second law, $\vec{F} = m\vec{a}$, requiring direction for force calculations.

Why the others are wrong:

• A: Distance is scalar, measuring total length without direction.
• B: Speed is scalar, the magnitude of velocity without direction.
• D: Time is scalar, a measure of duration without direction.

Final answer: C