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: Calculate the Acceleration To find the distance covered, we first need to calculate the acceleration of the car. We can use the formula for acceleration (\(a\)): \[ a = \frac{v - u}{t} \] 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 3: Use the Distance Formula Now that we have the acceleration, we can use the formula for distance (\(s\)) covered under uniform acceleration: \[ s = ut + \frac{1}{2} a t^2 \] Since the initial velocity \(u\) is 0, the formula simplifies to: \[ s = 0 \cdot t + \frac{1}{2} a t^2 = \frac{1}{2} a t^2 \] Substituting the values of \(a\) and \(t\): \[ s = \frac{1}{2} \cdot 4 \, \text{m/s}^2 \cdot (5 \, \text{s})^2 \] Calculating \(t^2\): \[ (5 \, \text{s})^2 = 25 \, \text{s}^2 \] Now substituting back into the distance formula: \[ s = \frac{1}{2} \cdot 4 \, \text{m/s}^2 \cdot 25 \, \text{s}^2 = 2 \cdot 25 = 50 \, \text{m} \] ### 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 - **Option A (25 meters)**: This option is incorrect because it underestimates the distance covered. It does not account for the full effect of the acceleration over the 5 seconds. - **Option C (100 meters)**: This option is incorrect as it overestimates the distance. It may arise from a misunderstanding of the acceleration or the time involved. - **Option D (200 meters)**: This option is also incorrect and represents a significant overestimation. It likely results from a miscalculation or misunderstanding of the uniform acceleration concept. ### Revision Summary - Use the formula \(s = ut + \frac{1}{2} a t^2\) for distance under uniform acceleration. - Calculate acceleration using \(a = \frac{v - u}{t}\). - Remember that if the initial velocity is zero, the formula simplifies to \(s = \frac{1}{2} a t^2\). - Always double-check calculations to avoid common pitfalls in physics problems.