To determine the distance covered by a car that accelerates uniformly from rest to a speed of 20 m/s in 10 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 (\(t\)) = 10 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: \[ a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = \frac{20 \, \text{m/s}}{10 \, \text{s}} = 2 \, \text{m/s}^2 \] ### 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: \[ s = (0 \, \text{m/s})(10 \, \text{s}) + \frac{1}{2} (2 \, \text{m/s}^2)(10 \, \text{s})^2 \] Calculating each term: - The first term is \(0\). - The second term is: \[ \frac{1}{2} \times 2 \, \text{m/s}^2 \times 100 \, \text{s}^2 = 1 \times 100 = 100 \, \text{m} \] ### Final Calculation Thus, the total distance covered by the car is: \[ s = 0 + 100 \, \text{m} = 100 \, \text{m} \] ### Conclusion The correct answer is **B. 100 meters**. ### Explanation of Other Options - **A. 50 meters**: This option is incorrect because it underestimates the distance covered. The calculations show that the car travels 100 meters, not 50. - **C. 200 meters**: This option is incorrect as it overestimates the distance. The calculations clearly indicate that the distance is 100 meters. - **D. 400 meters**: This option is also incorrect. It is significantly higher than the calculated distance, which is 100 meters. ### Common Pitfalls - **Forgetting to convert units**: Always ensure that the units are consistent (e.g., seconds for time, meters for distance). - **Misapplying the formula**: Ensure that you are using the correct formula for uniformly accelerated motion. - **Neglecting to calculate acceleration**: Always calculate acceleration if it is not given, as it is crucial for finding distance. ### 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 your final answer against the options provided.