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**: - The calculation shows that the acceleration is \( 1 \, \text{m/s}^2 \), which is not one of the options provided. Let's re-evaluate the equation used. ### Correct Approach: The correct equation to use is: \[ s = ut + \frac{1}{2} a t^2 \] However, we need to find time \( t \) first. We can use the formula: \[ v = u + at \] Since \( u = 0 \): \[ 20 = 0 + at \implies t = \frac{20}{a} \] Now substituting \( t \) back into the distance equation: \[ 200 = 0 + \frac{1}{2} a \left(\frac{20}{a}\right)^2 \] \[ 200 = \frac{1}{2} a \cdot \frac{400}{a^2} \] \[ 200 = \frac{200}{a} \] \[ a = 1 \, \text{m/s}^2 \] ### Conclusion: The correct answer is not among the options provided. The calculations consistently yield \( 1 \, \text{m/s}^2 \). ### Explanation of Options: - **A. 2 m/s²**: This would imply a different distance or time, which does not match the given conditions. - **B. 4 m/s²**: This is incorrect based on our calculations. - **C. 5 m/s²**: This would also imply a different distance or time, which does not match the given conditions. - **D. 10 m/s²**: This is too high for the given distance and final speed. ### Revision Summary: - Use the correct equations of motion based on the known variables. - Always check calculations for consistency. - Understand the relationships between distance, speed, and acceleration. - Be cautious of the units and ensure they are consistent throughout the calculations.