In introductory physics, which statement best explains acceleration?

• A. Acceleration is the amount of force an object has, measured in newtons.
• B. Acceleration is the rate of change of position with respect to time, $a=\frac{dx}{dt}$.
• C. Acceleration is the rate of change of velocity with respect to time, $a=\frac{dv}{dt}$.
• D. Acceleration is the total distance traveled divided by time, $a=\frac{d}{t}$.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definition of acceleration in physics. Acceleration is defined as the rate of change of velocity with respect to time.
2. Step 2: Recall that velocity itself is the rate of change of position with respect to time, so acceleration involves how velocity changes over time, not just position or distance.
3. Step 3: Express acceleration mathematically as \(a = \frac{d v}{d t}\), where \(v\) is velocity and \(t\) is time.
4. Step 4: Differentiate acceleration from other concepts: force is related to acceleration by Newton's second law (\(F = m a\)), but acceleration itself is not a force and is not measured in newtons.
5. Step 5: Recognize that acceleration is not the total distance divided by time (which is average speed), nor is it the rate of change of position (which is velocity). Therefore, the correct statement is that acceleration is the rate of change of velocity with respect to time.