To determine the final velocity of an object moving with constant acceleration, we can use the kinematic equation that relates initial velocity, acceleration, time, and final velocity. The equation is: \[ v = u + at \] Where: - \( v \) = final velocity (what we want to find) - \( u \) = initial velocity - \( a \) = acceleration - \( t \) = time ### Step-by-Step Explanation 1. **Identify the Given Values**: - Initial velocity (\( u \)) = 5 m/s - Acceleration (\( a \)) = 2 m/s² - Time (\( t \)) = 3 seconds 2. **Substitute the Values into the Equation**: We will substitute the known values into the kinematic equation: \[ v = 5 \, \text{m/s} + (2 \, \text{m/s}^2 \times 3 \, \text{s}) \] 3. **Calculate the Acceleration Component**: First, calculate the product of acceleration and time: \[ 2 \, \text{m/s}^2 \times 3 \, \text{s} = 6 \, \text{m/s} \] 4. **Add the Initial Velocity**: Now, add this result to the initial velocity: \[ v = 5 \, \text{m/s} + 6 \, \text{m/s} = 11 \, \text{m/s} \] 5. **Final Result**: Therefore, the final velocity after 3 seconds is: \[ v = 11 \, \text{m/s} \] ### Conclusion The correct answer is **A. 11 m/s**. ### Explanation of Other Options - **B. 8 m/s**: This option is incorrect because it does not account for the full effect of the acceleration over the 3 seconds. It seems to suggest a misunderstanding of how to apply the acceleration to the initial velocity. - **C. 17 m/s**: This option is incorrect as it implies an overestimation of the acceleration effect. It might result from incorrectly adding the acceleration multiple times or misunderstanding the time factor. - **D. 2 m/s**: This option is incorrect as it suggests a misunderstanding of the initial velocity and the effect of acceleration. It does not reflect any of the calculations we performed. ### Common Pitfalls - **Forgetting to multiply acceleration by time**: This is a common mistake. Always ensure you multiply the acceleration by the time to find the change in velocity. - **Confusing acceleration with velocity**: Remember that acceleration is the rate of change of velocity, not the velocity itself. - **Neglecting the initial velocity**: Always start with the initial velocity when calculating the final velocity. ### Revision Summary - Use the kinematic equation \( v = u + at \) to find final velocity. - Substitute known values carefully and perform calculations step-by-step. - Ensure to account for both initial velocity and the change in velocity due to acceleration. - Double-check calculations to avoid common mistakes.