To determine the final speed of the car after it accelerates for a certain period, we can use the basic kinematic equation that relates initial velocity, acceleration, time, and final velocity. The equation we will use is: \[ v_f = v_i + a \cdot t \] Where: - \( v_f \) = final velocity (what we are trying to find) - \( v_i \) = initial velocity - \( a \) = acceleration - \( t \) = time ### Step-by-Step Explanation 1. **Identify the Given Values**: - Initial speed (\( v_i \)): 20 m/s - Acceleration (\( a \)): 2 m/s² - Time (\( t \)): 5 seconds 2. **Substitute the Values into the Equation**: We will plug the values into the kinematic equation: \[ v_f = 20 \, \text{m/s} + (2 \, \text{m/s}^2 \cdot 5 \, \text{s}) \] 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 Speed to the Acceleration Component**: Now, add this result to the initial speed: \[ v_f = 20 \, \text{m/s} + 10 \, \text{m/s} = 30 \, \text{m/s} \] 5. **Final Result**: Therefore, the final speed of the car after 5 seconds of acceleration is: \[ v_f = 30 \, \text{m/s} \] ### Conclusion The correct answer is **B. 30 m/s**. ### Explanation of Other Options - **A. 20 m/s**: This option suggests that the car did not accelerate at all, which contradicts the information given that the car is accelerating at 2 m/s². - **C. 40 m/s**: This option would imply that the car accelerated at a much higher rate or for a longer time than stated. The calculations show that the maximum increase in speed due to the given acceleration and time is only 10 m/s. - **D. 10 m/s**: This option suggests a decrease in speed, which is impossible given that the car is accelerating. The initial speed is 20 m/s, and acceleration would only increase this speed. ### Common Pitfalls - **Misunderstanding Acceleration**: Some students may confuse acceleration with speed. Remember, acceleration is the rate of change of speed, not the speed itself. - **Forgetting to Convert Units**: Ensure that all units are consistent. In this case, all values are in meters and seconds, which is correct. - **Incorrectly Applying the Formula**: Always double-check that you are using the correct kinematic equation for the situation. ### 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. - Understand the physical meaning of acceleration and how it affects speed. - Always verify that your answer makes sense in the context of the problem.