To find the average rectilinear acceleration of the car, we can use the formula for average acceleration, which is defined as the change in velocity divided by the time taken for that change. The formula is: \[ a = \frac{\Delta v}{\Delta t} \] Where: - \( a \) is the average acceleration, - \( \Delta v \) is the change in velocity, - \( \Delta t \) is the change in time. ### Step-by-Step Calculation 1. **Identify the initial and final velocities**: - Initial velocity (\( v_i \)) = 20 m/s - Final velocity (\( v_f \)) = 50 m/s 2. **Calculate the change in velocity (\( \Delta v \))**: \[ \Delta v = v_f - v_i = 50 \, \text{m/s} - 20 \, \text{m/s} = 30 \, \text{m/s} \] 3. **Identify the time interval (\( \Delta t \))**: - The time taken for this change is given as 5 seconds. 4. **Substitute the values into the acceleration formula**: \[ a = \frac{\Delta v}{\Delta t} = \frac{30 \, \text{m/s}}{5 \, \text{s}} = 6 \, \text{m/s}^2 \] ### Conclusion The average rectilinear acceleration of the car during this time period is **6 m/s²**. Therefore, the correct option is **A**. ### Explanation of Other Options - **Option B (8 m/s²)**: This option is incorrect because it does not accurately reflect the calculated average acceleration. The calculation shows that the average acceleration is 6 m/s², not 8 m/s². - **Option C (5 m/s²)**: This option is also incorrect. It underestimates the average acceleration based on the change in velocity and time provided. The calculation clearly shows that the average acceleration is higher than 5 m/s². - **Option D (10 m/s²)**: This option is incorrect as well. It overestimates the average acceleration. The calculation indicates that the average acceleration is significantly lower than 10 m/s². ### Common Pitfalls - **Misunderstanding the formula**: Ensure you are using the correct formula for average acceleration. It is crucial to remember that acceleration is the change in velocity over time. - **Forgetting to subtract initial velocity from final velocity**: Always remember to calculate the change in velocity correctly by subtracting the initial velocity from the final velocity. - **Confusing units**: Make sure to keep track of the units (m/s for velocity and seconds for time) to avoid calculation errors. ### Revision Summary - Average acceleration is calculated using the formula \( a = \frac{\Delta v}{\Delta t} \). - Change in velocity is found by subtracting initial velocity from final velocity. - In this case, the average acceleration is 6 m/s². - Always double-check calculations and units to avoid common mistakes.