To determine the final velocity of a car that is initially traveling at 20 m/s and accelerates uniformly at a rate of 3 m/s² over a period of 5 seconds, we can use the formula for final velocity in uniformly accelerated motion: ### Formula: \[ v_f = v_i + a \cdot t \] Where: - \( v_f \) = final velocity - \( v_i \) = initial velocity - \( a \) = acceleration - \( t \) = time ### Step-by-Step Calculation: 1. **Identify the Given Values:** - Initial velocity (\( v_i \)) = 20 m/s - Acceleration (\( a \)) = 3 m/s² - Time (\( t \)) = 5 seconds 2. **Substitute the Values into the Formula:** \[ v_f = 20 \, \text{m/s} + (3 \, \text{m/s}^2 \cdot 5 \, \text{s}) \] 3. **Calculate the Acceleration Component:** - First, calculate \( 3 \, \text{m/s}^2 \cdot 5 \, \text{s} \): \[ 3 \cdot 5 = 15 \, \text{m/s} \] 4. **Add the Acceleration to the Initial Velocity:** \[ v_f = 20 \, \text{m/s} + 15 \, \text{m/s} = 35 \, \text{m/s} \] 5. **Final Result:** - The final velocity (\( v_f \)) after 5 seconds is **35 m/s**. ### Conclusion: The correct option is **A. 35 m/s**. ### Explanation of Other Options: - **B. 20 m/s**: This option represents the initial velocity and does not account for the acceleration over the 5 seconds. It is incorrect because it ignores the effect of the acceleration. - **C. 50 m/s**: This option is too high and suggests an incorrect calculation. It may arise from a misunderstanding of how to apply the acceleration over time. The correct calculation shows that the final velocity is 35 m/s, not 50 m/s. - **D. 25 m/s**: This option is also incorrect. It may result from incorrectly adding the acceleration or misunderstanding the time duration. The correct calculation shows that the final velocity is significantly higher than 25 m/s. ### Common Pitfalls: - **Ignoring the acceleration**: Some students may forget to include the acceleration in their calculations, leading to an incorrect final velocity. - **Miscalculating the time**: Ensure that the time is correctly multiplied by the acceleration. - **Confusing initial and final velocities**: Remember that the initial velocity is the starting point, and the final velocity is what we are calculating after the acceleration has taken effect. ### Revision Summary: - Use the formula \( v_f = v_i + a \cdot t \) for uniformly accelerated motion. - Substitute the initial velocity, acceleration, and time correctly. - Calculate the change in velocity due to acceleration before adding it to the initial velocity. - Always double-check calculations to avoid common mistakes.