To determine 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**: - The car starts from rest, so the initial velocity (\( v_i \)) is 0 m/s. - The final velocity (\( v_f \)) is given as 30 m/s. 2. **Calculate the Change in Velocity (\( \Delta v \))**: \[ \Delta v = v_f - v_i = 30 \, \text{m/s} - 0 \, \text{m/s} = 30 \, \text{m/s} \] 3. **Identify the Time Interval (\( \Delta t \))**: - The time taken to reach this speed is given as 10 seconds. 4. **Calculate the Average Acceleration (\( a \))**: \[ a = \frac{\Delta v}{\Delta t} = \frac{30 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}^2 \] ### Conclusion The average rectilinear acceleration of the car during this time period is **3 m/s²**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A (1 m/s²)**: This value would imply a much smaller change in velocity over the time period. If the acceleration were 1 m/s², the car would only reach a speed of 10 m/s in 10 seconds, which is incorrect. - **Option B (2 m/s²)**: This option suggests that the car would reach a speed of 20 m/s in 10 seconds, which again does not match the given final speed of 30 m/s. Thus, this option is also incorrect. - **Option D (4 m/s²)**: If the acceleration were 4 m/s², the car would reach a speed of 40 m/s in 10 seconds, which exceeds the final speed of 30 m/s. Therefore, this option is also incorrect. ### Common Pitfalls - **Misunderstanding the Formula**: Students sometimes confuse average acceleration with instantaneous acceleration. Average acceleration is calculated over a time interval, while instantaneous acceleration is the acceleration at a specific moment. - **Forgetting to Convert Units**: Ensure that all units are consistent. In this case, we used meters per second (m/s) for velocity and seconds (s) for time, which is correct. - **Not Accounting for Starting from Rest**: Remember that starting from rest means the initial velocity is zero, which is crucial for calculating the change in velocity. ### Revision Summary - Average acceleration is calculated using the formula \( a = \frac{\Delta v}{\Delta t} \). - The change in velocity is the final velocity minus the initial velocity. - In this case, the average acceleration is \( 3 \, \text{m/s}^2 \). - Always check that your calculations align with the physical scenario described in the problem.