To determine the distance covered by a car that accelerates uniformly from rest to a speed of 20 m/s in 5 seconds, we can use the equations of motion. Let's break this down step-by-step. ### Step 1: Identify the Given Information - Initial velocity (\(u\)) = 0 m/s (the car starts from rest) - Final velocity (\(v\)) = 20 m/s - Time (\(t\)) = 5 seconds ### Step 2: Use the Formula for Distance When an object accelerates uniformly, the distance (\(s\)) covered can be calculated using the formula: \[ s = ut + \frac{1}{2} a t^2 \] where: - \(s\) = distance covered - \(u\) = initial velocity - \(a\) = acceleration - \(t\) = time ### Step 3: Calculate the Acceleration First, we need to find the acceleration (\(a\)). We can use the formula: \[ a = \frac{v - u}{t} \] Substituting the known values: \[ a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{s}} = \frac{20 \, \text{m/s}}{5 \, \text{s}} = 4 \, \text{m/s}^2 \] ### Step 4: Substitute Values into the Distance Formula Now that we have the acceleration, we can substitute \(u\), \(a\), and \(t\) into the distance formula: \[ s = (0 \, \text{m/s})(5 \, \text{s}) + \frac{1}{2} (4 \, \text{m/s}^2)(5 \, \text{s})^2 \] Calculating the first term: \[ (0 \, \text{m/s})(5 \, \text{s}) = 0 \, \text{m} \] Calculating the second term: \[ \frac{1}{2} (4 \, \text{m/s}^2)(25 \, \text{s}^2) = \frac{1}{2} (4 \times 25) \, \text{m} = \frac{1}{2} (100) \, \text{m} = 50 \, \text{m} \] ### Step 5: Combine the Results Adding both terms together: \[ s = 0 \, \text{m} + 50 \, \text{m} = 50 \, \text{m} \] ### Conclusion The distance covered by the car during the 5 seconds of acceleration is **50 meters**. Therefore, the correct option is **B**. ### Explanation of Other Options - **A. 25 meters**: This option is incorrect because it underestimates the distance covered. The calculations show that the car travels 50 meters, not 25. - **C. 100 meters**: This option is incorrect as it overestimates the distance. The calculations clearly indicate that the distance is 50 meters, not 100. - **D. 200 meters**: This option is also incorrect and significantly overestimates the distance. The physics of uniform acceleration and the calculations confirm that the distance is only 50 meters. ### Common Pitfalls - **Forgetting to convert units**: Ensure all units are consistent (e.g., time in seconds, distance in meters). - **Misapplying the formula**: Remember that the initial velocity is zero when starting from rest. - **Not calculating acceleration correctly**: Always double-check the calculation of acceleration using the correct formula. ### Revision Summary - Use the formula \(s = ut + \frac{1}{2} a t^2\) for distance under uniform acceleration. - Calculate acceleration using \(a = \frac{v - u}{t}\). - Substitute values carefully and perform calculations step-by-step. - Always verify your final answer against the options provided.