To determine the final velocity of an object moving in a straight line 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 (\( u \)) = 10 m/s - Acceleration (\( a \)) = 4 m/s² - Time (\( t \)) = 3 seconds 2. **Substitute the Values into the Equation**: We will substitute the known values into the kinematic equation: \[ v = 10 \, \text{m/s} + (4 \, \text{m/s}^2 \times 3 \, \text{s}) \] 3. **Calculate the Acceleration Component**: First, calculate the product of acceleration and time: \[ 4 \, \text{m/s}^2 \times 3 \, \text{s} = 12 \, \text{m/s} \] 4. **Add the Initial Velocity**: Now, add this result to the initial velocity: \[ v = 10 \, \text{m/s} + 12 \, \text{m/s} = 22 \, \text{m/s} \] 5. **Final Result**: Therefore, the final velocity after 3 seconds is: \[ v = 22 \, \text{m/s} \] ### Conclusion The correct option is **A. 22 m/s**. ### Explanation of Other Options - **B. 10 m/s**: This option represents the initial velocity and does not account for the acceleration over time. It is incorrect because it ignores the effect of the constant acceleration. - **C. 34 m/s**: This option is too high and suggests an incorrect calculation. It may arise from mistakenly adding the acceleration multiple times or miscalculating the time factor. - **D. 16 m/s**: This option is also incorrect. It may result from a misunderstanding of how to apply the acceleration over time or miscalculating the addition of the acceleration component. ### Common Pitfalls - **Ignoring the effect of acceleration**: Some students may forget to include the acceleration when calculating the final velocity. - **Misapplying the formula**: Ensure that the correct kinematic equation is used and that all units are consistent (e.g., m/s for velocity and m/s² for acceleration). - **Calculation errors**: Double-check arithmetic operations, especially when multiplying acceleration by time. ### Revision Summary - Use the kinematic equation \( v = u + at \) to find final velocity. - Substitute known values carefully and perform calculations step-by-step. - Understand the role of acceleration in changing the velocity over time. - Review common mistakes to avoid errors in future problems.