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 (30 m/s) - \( u \) = initial velocity (0 m/s, since the car starts from rest) - \( a \) = acceleration (what we are trying to find) - \( s \) = distance (180 m) ### Step-by-Step Solution: 1. **Identify the known values**: - Initial velocity, \( u = 0 \, \text{m/s} \) - Final velocity, \( v = 30 \, \text{m/s} \) - Distance, \( s = 180 \, \text{m} \) 2. **Substitute the known values into the equation**: \[ (30 \, \text{m/s})^2 = (0 \, \text{m/s})^2 + 2a(180 \, \text{m}) \] 3. **Calculate \( v^2 \)**: \[ 900 \, \text{m}^2/\text{s}^2 = 0 + 360a \] 4. **Rearrange the equation to solve for \( a \)**: \[ 900 = 360a \] \[ a = \frac{900}{360} \] \[ a = 2.5 \, \text{m/s}^2 \] 5. **Check the calculations**: - The calculation shows that the acceleration is \( 2.5 \, \text{m/s}^2 \), which does not match any of the provided options. Therefore, let's re-evaluate the problem. ### Re-evaluation of the Problem: Upon reviewing the calculations, it appears that the initial interpretation of the problem was correct, but the options provided do not include the correct answer. ### Explanation of the Options: - **Option A (5 m/s²)**: This is incorrect because, based on our calculations, the acceleration is \( 2.5 \, \text{m/s}^2 \). - **Option B (10 m/s²)**: This is also incorrect. It is too high for the given distance and final speed. - **Option C (15 m/s²)**: This is incorrect as well. It would imply a much shorter distance to reach 30 m/s. - **Option D (20 m/s²)**: This is incorrect. It would require an even shorter distance to reach the final speed. ### Common Pitfalls: - **Misunderstanding the equations of motion**: It's crucial to use the correct equation based on the known variables. - **Forgetting to convert units**: Always ensure that all units are consistent (e.g., meters and seconds). - **Rounding errors**: Be careful with calculations to avoid rounding too early. ### Revision Summary: - Use the equation \( v^2 = u^2 + 2as \) to relate velocity, acceleration, and distance. - Ensure all values are correctly substituted and calculated. - Double-check the final answer against the provided options. - Understand that if the calculated answer does not match the options, there may be an error in the options provided. In conclusion, the correct acceleration based on the calculations is \( 2.5 \, \text{m/s}^2 \), which is not listed among the options.