To find the car's acceleration, we can use one of the equations of motion that relates initial velocity, final velocity, acceleration, and distance. The equation we will use is: \[ v^2 = u^2 + 2as \] Where: - \( v \) = final velocity (25 m/s) - \( u \) = initial velocity (0 m/s, since the car starts from rest) - \( a \) = acceleration (what we are trying to find) - \( s \) = distance (200 m) ### Step-by-Step Solution: 1. **Identify the known values**: - Final velocity, \( v = 25 \, \text{m/s} \) - Initial velocity, \( u = 0 \, \text{m/s} \) - Distance, \( s = 200 \, \text{m} \) 2. **Substitute the known values into the equation**: \[ (25 \, \text{m/s})^2 = (0 \, \text{m/s})^2 + 2a(200 \, \text{m}) \] 3. **Calculate \( v^2 \)**: \[ 625 \, \text{m}^2/\text{s}^2 = 0 + 400a \] 4. **Rearrange the equation to solve for \( a \)**: \[ 625 = 400a \] \[ a = \frac{625}{400} \] 5. **Perform the division**: \[ a = 1.5625 \, \text{m/s}^2 \] 6. **Round to two decimal places**: \[ a \approx 1.56 \, \text{m/s}^2 \] ### Conclusion: The correct answer is **A. 1.56 m/s²**. ### Explanation of Other Options: - **Option B (3.12 m/s²)**: This value is incorrect because it likely results from a miscalculation or misunderstanding of the relationship between distance, velocity, and acceleration. It does not satisfy the equation of motion used. - **Option C (6.25 m/s²)**: This value is also incorrect. It may arise from incorrectly assuming a different relationship or misapplying the formula. It does not fit the context of the problem. - **Option D (12.5 m/s²)**: This option is significantly higher than the calculated acceleration. It could be a result of misunderstanding the units or the relationship between the variables involved. ### Common Pitfalls: - **Forgetting to square the final velocity**: When using the equation \( v^2 = u^2 + 2as \), it’s crucial to remember that \( v \) must be squared. - **Misunderstanding the initial conditions**: Always ensure that the initial velocity is correctly identified, especially if the object starts from rest. - **Not rearranging the equation correctly**: When solving for acceleration, ensure that all terms are correctly isolated. ### Revision Summary: - Use the equation \( v^2 = u^2 + 2as \) to relate velocity, acceleration, and distance. - Substitute known values carefully and perform calculations step-by-step. - Be cautious of common mistakes, such as squaring values and rearranging equations. - The final answer for the car's acceleration in this scenario is **1.56 m/s²**.