To determine the distance traveled by a car that accelerates uniformly from rest to a speed of 30 m/s in 10 seconds, we can use the equations of motion. Let's break down the problem step-by-step. ### Step 1: Identify the Given Information - Initial velocity (\(u\)): 0 m/s (the car starts from rest) - Final velocity (\(v\)): 30 m/s - Time (\(t\)): 10 seconds ### Step 2: Calculate the Acceleration To find the distance traveled, 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: \[ a = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = \frac{30 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}^2 \] ### Step 3: Calculate the Distance Traveled Now that we have the acceleration, we can use the formula for distance (\(s\)) traveled 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 \(t\): \[ s = \frac{1}{2} \cdot 3 \, \text{m/s}^2 \cdot (10 \, \text{s})^2 \] Calculating further: \[ s = \frac{1}{2} \cdot 3 \cdot 100 = \frac{300}{2} = 150 \, \text{meters} \] ### Conclusion The distance traveled by the car during the 10 seconds of acceleration is **150 meters**. Therefore, the correct option is **A. 150 meters**. ### Explanation of Other Options - **B. 300 meters**: This option is incorrect because it assumes a different calculation, possibly misapplying the formula or misunderstanding the relationship between speed, time, and distance. - **C. 200 meters**: This option is also incorrect. It may arise from a miscalculation or incorrect assumptions about the acceleration or time. - **D. 100 meters**: This option is incorrect as well. It could be a result of halving the correct distance or misunderstanding the acceleration's effect over time. ### Common Pitfalls - **Forgetting to convert units**: Always ensure that all units are consistent (e.g., seconds for time, meters for distance). - **Misapplying the equations of motion**: Ensure you are using the correct formula based on the initial conditions (like starting from rest). - **Confusing distance with displacement**: In this case, since the car is moving in a straight line and starting from rest, distance and displacement are the same. ### Revision Summary - Use the formula \(s = ut + \frac{1}{2} a t^2\) for distance under uniform acceleration. - Calculate acceleration using \(a = \frac{v - u}{t}\). - Ensure all units are consistent and correctly applied. - Double-check calculations to avoid common mistakes.