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 (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 \( a = 1 \, \text{m/s}^2 \), but this does not match any of the options provided. Let's re-evaluate the equation used. ### Correct Approach: The correct equation to use is: \[ s = ut + \frac{1}{2} a t^2 \] And we also need to find the time \( t \) using: \[ v = u + at \] 1. **From the first equation**: Since \( u = 0 \): \[ s = \frac{1}{2} a t^2 \] 2. **From the second equation**: \[ v = at \implies t = \frac{v}{a} \] 3. **Substituting \( t \) into the first equation**: \[ s = \frac{1}{2} a \left(\frac{v}{a}\right)^2 \] \[ s = \frac{1}{2} a \frac{v^2}{a^2} = \frac{v^2}{2a} \] 4. **Rearranging to find \( a \)**: \[ 2as = v^2 \implies a = \frac{v^2}{2s} \] 5. **Substituting the known values**: \[ a = \frac{(20 \, \text{m/s})^2}{2 \times 200 \, \text{m}} = \frac{400}{400} = 1 \, \text{m/s}^2 \] ### Conclusion: The correct answer is **not** among the options provided. The calculated acceleration is \( 1 \, \text{m/s}^2 \). ### Explanation of Options: - **A. 2 m/s²**: This would imply a much faster acceleration over the same distance, which is incorrect based on our calculations. - **B. 4 m/s²**: This is incorrect as it suggests a higher acceleration than what is calculated. - **C. 5 m/s²**: This is also incorrect for the same reasons as above. - **D. 10 m/s²**: This would imply an extremely rapid acceleration, which is not supported by the data. ### Revision Summary: - Use the correct equations of motion to relate distance, velocity, and acceleration. - Always check the units and ensure they are consistent. - If the calculated answer does not match the options, re-evaluate the approach or check for any misinterpretation of the problem. - Remember that acceleration can be calculated using \( a = \frac{v^2}{2s} \) when starting from rest.