To find the magnitude of 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 (20 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**: - Initial velocity, \( u = 0 \, \text{m/s} \) - Final velocity, \( v = 20 \, \text{m/s} \) - Distance, \( s = 200 \, \text{m} \) 2. **Substitute the known values into the equation**: \[ (20 \, \text{m/s})^2 = (0 \, \text{m/s})^2 + 2a(200 \, \text{m}) \] 3. **Calculate \( v^2 \)**: \[ 400 \, \text{m}^2/\text{s}^2 = 0 + 400a \] 4. **Rearrange the equation to solve for \( a \)**: \[ 400 = 400a \] \[ a = \frac{400}{400} = 1 \, \text{m/s}^2 \] 5. **Check the calculation**: - We have \( 400 = 400a \), which simplifies correctly to \( a = 1 \, \text{m/s}^2 \). ### Conclusion: The magnitude of the car's acceleration is **1 m/s²**. However, it seems there was a misunderstanding in the options provided. The correct answer is not listed among the options A, B, C, or D. ### Explanation of Other Options: - **Option A (2 m/s²)**: This would imply that the car could reach 20 m/s in a shorter distance than 200 m, which is incorrect based on the calculations. - **Option B (4 m/s²)**: This would suggest that the car could reach 20 m/s in even less distance, which contradicts the given distance of 200 m. - **Option C (5 m/s²)**: This would also imply a much shorter distance to reach 20 m/s, which is not supported by the calculations. - **Option D (10 m/s²)**: This would mean the car could reach 20 m/s almost instantaneously, which is not feasible given the distance. ### Common Pitfalls: - **Misunderstanding the equations of motion**: It's crucial to use the correct equation that relates the variables involved. - **Forgetting to square the final velocity**: When substituting values, ensure that you square the final velocity correctly. - **Not checking units**: Always ensure that the units are consistent (e.g., meters and seconds). ### Revision Summary: - Use the equation \( v^2 = u^2 + 2as \) to relate velocity, acceleration, and distance. - Substitute known values carefully and solve for the unknown. - Always double-check calculations for accuracy. - Understand the physical meaning of the results to avoid misinterpretation.