To find the final velocity of an object that is accelerating at a constant rate, we can use the following kinematic equation: \[ v_f = v_i + a \cdot t \] Where: - \( v_f \) = final velocity - \( v_i \) = initial velocity - \( a \) = acceleration - \( t \) = time ### Step-by-Step Explanation 1. **Identify the Given Values**: - Initial velocity (\( v_i \)): 10 m/s - Acceleration (\( a \)): 2 m/s² - Time (\( t \)): 5 seconds 2. **Substitute the Values into the Formula**: We will substitute the known values into the kinematic equation: \[ v_f = 10 \, \text{m/s} + (2 \, \text{m/s}^2 \cdot 5 \, \text{s}) \] 3. **Calculate the Acceleration Component**: First, calculate the product of acceleration and time: \[ 2 \, \text{m/s}^2 \cdot 5 \, \text{s} = 10 \, \text{m/s} \] 4. **Add the Initial Velocity**: Now, add this result to the initial velocity: \[ v_f = 10 \, \text{m/s} + 10 \, \text{m/s} = 20 \, \text{m/s} \] 5. **Final Result**: Therefore, the final velocity (\( v_f \)) of the object after 5 seconds is: \[ v_f = 20 \, \text{m/s} \] ### Conclusion The correct answer is **B. 20 m/s**. ### Explanation of Other Options - **A. 10 m/s**: This option represents the initial velocity and does not account for the acceleration over time. Since the object is accelerating, the final velocity must be greater than the initial velocity. - **C. 30 m/s**: This option incorrectly assumes a different calculation of acceleration or time. The correct calculation shows that the final velocity is 20 m/s, not 30 m/s. - **D. 40 m/s**: This option suggests an even higher final velocity, which would imply a much greater acceleration or longer time than what is given. The calculations clearly show that the final velocity is 20 m/s. ### Common Pitfalls - **Ignoring the acceleration**: Some students might forget to include the acceleration in their calculations, leading to incorrect answers. - **Miscalculating the time**: Ensure that the time is correctly applied in the formula; it is crucial for determining the change in velocity. - **Confusing initial and final velocities**: Remember that the initial velocity is the starting point, and the final velocity is what we are solving for after applying acceleration over time. ### Revision Summary - Use the kinematic equation \( v_f = v_i + a \cdot t \) to find final velocity. - Substitute known values carefully and perform calculations step-by-step. - Ensure to account for both initial velocity and the effect of acceleration over time. - Double-check calculations to avoid common mistakes in applying the formula.