To determine the car's acceleration, we can use the formula for acceleration in uniformly accelerated motion. The formula is: \[ a = \frac{\Delta v}{\Delta t} \] where: - \( a \) is the acceleration, - \( \Delta v \) is the change in velocity, - \( \Delta t \) is the change in time. ### Step-by-Step Explanation 1. **Identify the Initial and Final Velocities**: - The car starts from rest, so the initial velocity (\( v_i \)) is 0 m/s. - The final velocity (\( v_f \)) is given as 30 m/s. 2. **Calculate the Change in Velocity (\( \Delta v \))**: - The change in velocity is calculated as: \[ \Delta v = v_f - v_i = 30 \, \text{m/s} - 0 \, \text{m/s} = 30 \, \text{m/s} \] 3. **Identify the Time Interval (\( \Delta t \))**: - The time taken to reach this speed is given as 10 seconds. 4. **Substitute Values into the Acceleration Formula**: - Now we can substitute the values into the acceleration formula: \[ a = \frac{\Delta v}{\Delta t} = \frac{30 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}^2 \] 5. **Conclusion**: - The calculated acceleration of the car is \( 3 \, \text{m/s}^2 \). ### Why the Correct Option is C (3 m/s²) The correct answer is **C (3 m/s²)** because we followed the correct steps to calculate the acceleration based on the change in velocity and the time taken. The formula used is appropriate for uniformly accelerated motion, and the values substituted were accurate. ### Explanation of Other Options - **Option A (1 m/s²)**: This option is incorrect because it suggests that the car's acceleration is much lower than what we calculated. If the acceleration were 1 m/s², the car would only reach a speed of 10 m/s in 10 seconds, which contradicts the given final speed of 30 m/s. - **Option B (2 m/s²)**: This option is also incorrect. If the car had an acceleration of 2 m/s², it would reach a final speed of only 20 m/s in 10 seconds, which again does not match the given final speed of 30 m/s. - **Option D (4 m/s²)**: This option is incorrect as well. An acceleration of 4 m/s² would result in a final speed of 40 m/s in 10 seconds, which exceeds the given final speed of 30 m/s. ### Common Pitfalls - **Misunderstanding the Formula**: It's crucial to remember that acceleration is the change in velocity over time. Confusing this with other kinematic equations can lead to incorrect answers. - **Forgetting Initial Conditions**: Always ensure to account for the initial velocity, especially when it is zero, as in this case. - **Units**: Ensure that the units are consistent (e.g., m/s for velocity and seconds for time) to avoid calculation errors. ### Revision Summary - Acceleration is calculated using the formula \( a = \frac{\Delta v}{\Delta t} \). - For this problem, the change in velocity is 30 m/s, and the time is 10 seconds. - The correct acceleration is \( 3 \, \text{m/s}^2 \) (Option C). - Always check initial conditions and ensure units are consistent to avoid mistakes.