To determine the final velocity of an object moving in a straight line with constant acceleration, we can use the following kinematic equation: \[ v = u + at \] Where: - \( v \) = final velocity (m/s) - \( u \) = initial velocity (m/s) - \( a \) = acceleration (m/s²) - \( t \) = time (s) ### Step-by-Step Explanation 1. **Identify the Given Values**: - Initial velocity (\( u \)) = 5 m/s - Acceleration (\( a \)) = 2 m/s² - Time (\( t \)) = 3 s 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 of the object after 3 seconds is: \[ v = 11 \, \text{m/s} \] ### Conclusion The correct answer is **B. 11 m/s**. ### Explanation of Other Options - **Option A (8 m/s)**: This option is incorrect because it does not account for the full effect of the acceleration over the 3 seconds. It suggests that the object has decelerated or that the acceleration was not applied correctly. - **Option C (14 m/s)**: This option is also incorrect. It implies that the acceleration was applied for a longer duration or at a higher rate than given, which is not the case here. - **Option D (17 m/s)**: This option is incorrect as well. It suggests an overestimation of the final velocity, possibly by miscalculating the acceleration component or misunderstanding the initial conditions. ### Common Pitfalls - **Misunderstanding the Equation**: Students sometimes confuse the kinematic equations or forget to add the initial velocity to the product of acceleration and time. - **Neglecting Units**: Always ensure that the units are consistent (e.g., m/s for velocity, m/s² for acceleration). - **Forgetting Initial Conditions**: The initial velocity is crucial in determining the final velocity; neglecting it can lead to incorrect answers. ### Revision Summary - Use the kinematic equation \( v = u + at \) to find final velocity. - Substitute known values carefully and perform calculations step-by-step. - Always include the initial velocity in your calculations. - Check your units to ensure consistency throughout the problem.