To determine the car's rectilinear acceleration, we can use the basic kinematic equation that relates acceleration, initial velocity, final velocity, and time. The equation we will use is: \[ a = \frac{v_f - v_i}{t} \] Where: - \( a \) is the acceleration, - \( v_f \) is the final velocity, - \( v_i \) is the initial velocity, - \( t \) is the time taken. ### Step-by-Step Explanation 1. **Identify the Given Values**: - The car starts from rest, so the initial velocity \( v_i = 0 \, \text{m/s} \). - The final velocity \( v_f = 20 \, \text{m/s} \). - The time taken to reach this speed \( t = 5 \, \text{s} \). 2. **Substitute the Values into the Formula**: We can now substitute the known values into the acceleration formula: \[ a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{s}} \] 3. **Calculate the Acceleration**: \[ a = \frac{20 \, \text{m/s}}{5 \, \text{s}} = 4 \, \text{m/s}^2 \] Thus, the car's rectilinear acceleration is **4 m/s²**. ### Why Option B is Correct - The calculation shows that the acceleration is \( 4 \, \text{m/s}^2 \), which corresponds to option B. This means that for every second, the car's speed increases by 4 meters per second. ### Explanation of Other Options - **Option A: 2 m/s²**: This option is incorrect because if the acceleration were 2 m/s², the car would only reach a speed of \( 2 \, \text{m/s} \times 5 \, \text{s} = 10 \, \text{m/s} \) after 5 seconds, which is not the final speed given in the problem. - **Option C: 5 m/s²**: This option is also incorrect. If the acceleration were 5 m/s², the car would reach a speed of \( 5 \, \text{m/s} \times 5 \, \text{s} = 25 \, \text{m/s} \) after 5 seconds, which exceeds the final speed of 20 m/s. - **Option D: 10 m/s²**: This option is incorrect as well. An acceleration of 10 m/s² would result in a final speed of \( 10 \, \text{m/s} \times 5 \, \text{s} = 50 \, \text{m/s} \), which is far greater than the specified final speed of 20 m/s. ### Common Pitfalls - **Misunderstanding Initial Conditions**: Always ensure you correctly identify the initial velocity, especially if the object starts from rest. - **Forgetting to Use the Correct Formula**: Make sure to use the appropriate kinematic equations for uniformly accelerated motion. - **Units**: Be careful with units; ensure that time is in seconds and speed is in meters per second to maintain consistency. ### Revision Summary - The formula for acceleration is \( a = \frac{v_f - v_i}{t} \). - For this problem, \( v_i = 0 \, \text{m/s} \), \( v_f = 20 \, \text{m/s} \), and \( t = 5 \, \text{s} \). - The calculated acceleration is \( 4 \, \text{m/s}^2 \), which corresponds to option B. - Always check your calculations and ensure you understand the physical meaning of the variables involved.