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 (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 (100 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, \( s = 100 \, \text{m} \) 2. **Substitute the known values into the equation**: \[ (20 \, \text{m/s})^2 = (0 \, \text{m/s})^2 + 2a(100 \, \text{m}) \] 3. **Calculate \( v^2 \)**: \[ 400 \, \text{m}^2/\text{s}^2 = 0 + 200a \] 4. **Rearrange the equation to solve for \( a \)**: \[ 400 = 200a \] \[ a = \frac{400}{200} = 2 \, \text{m/s}^2 \] ### Conclusion: The car's acceleration is \( 2 \, \text{m/s}^2 \). Therefore, the correct option is **A**. ### Explanation of Other Options: - **Option B (4 m/s²)**: This option is incorrect because it suggests a higher acceleration than what is calculated. If the acceleration were 4 m/s², the car would reach a higher speed over the same distance, which contradicts the given final speed of 20 m/s. - **Option C (5 m/s²)**: This option is also incorrect for similar reasons. An acceleration of 5 m/s² would result in a final speed that exceeds 20 m/s over 100 meters, indicating that the car would have accelerated too quickly. - **Option D (10 m/s²)**: This option is incorrect as well. An acceleration of 10 m/s² would lead to an even higher final speed, making it impossible for the car to reach only 20 m/s over 100 meters. ### Common Pitfalls: - **Misunderstanding the equation**: It's crucial to use the correct equation of motion. The equation \( v^2 = u^2 + 2as \) is specifically designed for uniformly accelerated motion. - **Forgetting to square the final velocity**: When substituting values, ensure that you square the final velocity correctly. - **Confusing distance with displacement**: In this context, distance is the total path length, which is important for calculating acceleration. ### Revision Summary: - Use the equation \( v^2 = u^2 + 2as \) for uniformly accelerated motion. - Ensure to substitute values correctly and perform calculations step-by-step. - Understand that acceleration affects how quickly an object reaches its final speed over a given distance. - Double-check calculations to avoid common mistakes, such as misapplying formulas or miscalculating squares.