In one-dimensional motion, which scenario is an example of negative acceleration (taking the positive direction to be to the right)?

• A. A car moving to the left slows from $20\text{m/s}$ to $10\text{m/s}$ in $5\text{s}$.
• B. A car moving to the right slows from $20\text{m/s}$ to $10\text{m/s}$ in $5\text{s}$.
• C. An object moves to the right at a constant velocity of $15\text{m/s}$ for $10\text{s}$.
• D. A car moving to the right speeds up from $10\text{m/s}$ to $20\text{m/s}$ in $5\text{s}$.

Answer: (B)

Verified step by step guidance

1. Recall that acceleration is defined as the rate of change of velocity with respect to time: \(a = \frac{\Delta v}{\Delta t}\).
2. Since velocity is a vector quantity, it has both magnitude and direction. Here, the positive direction is to the right.
3. Negative acceleration means the acceleration vector points opposite to the positive direction. This can happen if the velocity decreases while moving to the right, or if the velocity increases while moving to the left.
4. Analyze each scenario by considering the initial and final velocities and their directions, then calculate the change in velocity \(\Delta v = v_{final} - v_{initial}\).
5. Identify the scenario where the velocity decreases while moving to the right, resulting in a negative acceleration (deceleration in the positive direction).