To determine the car's rectilinear acceleration, we can use the basic kinematic equation that relates acceleration, initial velocity, final velocity, and time. Let's break this down step-by-step. ### Step 1: Identify the Given Information - **Initial velocity (u)**: The car starts from rest, so \( u = 0 \, \text{m/s} \). - **Final velocity (v)**: The car accelerates to a speed of \( v = 30 \, \text{m/s} \). - **Time (t)**: The time taken to reach this speed is \( t = 10 \, \text{s} \). ### Step 2: Use the Formula for Acceleration The formula for acceleration (\( a \)) when you know the initial velocity, final velocity, and time is given by: \[ a = \frac{v - u}{t} \] ### Step 3: Substitute the Values into the Formula Now, we can substitute the values we have into the formula: \[ a = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} \] ### Step 4: Perform the Calculation Calculating the numerator: \[ 30 \, \text{m/s} - 0 \, \text{m/s} = 30 \, \text{m/s} \] Now, divide by the time: \[ a = \frac{30 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}^2 \] ### Conclusion Thus, the car's rectilinear acceleration is \( 3 \, \text{m/s}^2 \). Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (2 m/s²)**: This value is too low. If the acceleration were 2 m/s², the car would not reach 30 m/s in 10 seconds. Using the same formula, \( a = 2 \, \text{m/s}^2 \) would yield a final speed of only \( 20 \, \text{m/s} \) after 10 seconds. - **Option C (5 m/s²)**: This value is too high. If the acceleration were 5 m/s², the car would reach a final speed of \( 50 \, \text{m/s} \) in 10 seconds, which exceeds the given final speed of 30 m/s. - **Option D (6 m/s²)**: This value is also too high. An acceleration of 6 m/s² would result in a final speed of \( 60 \, \text{m/s} \) after 10 seconds, which again is not consistent with the problem statement. ### Common Pitfalls - **Misunderstanding the initial conditions**: Remember that the car starts from rest, which means the initial velocity is zero. - **Forgetting to convert units**: Ensure that all units are consistent (e.g., time in seconds, speed in meters per second). - **Confusing acceleration with speed**: Acceleration is the change in speed over time, not the final speed itself. ### Revision Summary - The formula for acceleration is \( a = \frac{v - u}{t} \). - For this problem, \( u = 0 \, \text{m/s} \), \( v = 30 \, \text{m/s} \), and \( t = 10 \, \text{s} \). - The calculated acceleration is \( 3 \, \text{m/s}^2 \), making option B the correct answer. - Always check the reasonableness of your answer by considering the context of the problem.