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 each term: - The first term is \(0\). - The second term is: \[ \frac{1}{2} \times 4 \, \text{m/s}^2 \times 25 \, \text{s}^2 = 2 \times 25 = 50 \, \text{m} \] ### Final Calculation Thus, the total distance covered by the car is: \[ s = 0 + 50 \, \text{m} = 50 \, \text{m} \] ### Conclusion The correct answer is **B. 50 meters**. ### Explanation of Other Options - **A. 25 meters**: This option is incorrect because it underestimates the distance covered. It may arise from miscalculating the acceleration or not using the correct formula. - **C. 100 meters**: This option is incorrect as it overestimates the distance. It could result from incorrectly assuming a higher acceleration or misapplying the distance formula. - **D. 200 meters**: This option is also incorrect and represents a significant overestimation. It may come from a misunderstanding of the relationship between speed, time, and distance. ### Common Pitfalls - Forgetting to convert units or misinterpreting the time or speed. - Not recognizing that the car starts from rest, which means the initial velocity is zero. - Misapplying the formula for distance in uniformly accelerated motion. ### Revision Summary - Use the formula \(s = ut + \frac{1}{2} a t^2\) for uniformly accelerated motion. - Calculate acceleration using \(a = \frac{v - u}{t}\). - Substitute values carefully to avoid calculation errors. - Always check if the initial velocity is zero when the object starts from rest.