To determine how far the car travels in the first 5 seconds while accelerating uniformly from rest at a rate of 3 m/s², we can use the equations of motion. Specifically, we will use the second equation of motion, which relates distance, initial velocity, acceleration, and time. ### Step-by-Step Explanation 1. **Identify the Variables**: - Initial velocity (u): Since the car starts from rest, \( u = 0 \, \text{m/s} \). - Acceleration (a): The car accelerates at \( a = 3 \, \text{m/s}^2 \). - Time (t): We are interested in the distance traveled in \( t = 5 \, \text{s} \). 2. **Use the Equation of Motion**: The equation that relates these variables is: \[ s = ut + \frac{1}{2} a t^2 \] where: - \( s \) is the distance traveled, - \( u \) is the initial velocity, - \( a \) is the acceleration, - \( t \) is the time. 3. **Substitute the Values**: Plugging in the values we have: \[ s = (0 \, \text{m/s}) \cdot (5 \, \text{s}) + \frac{1}{2} (3 \, \text{m/s}^2) (5 \, \text{s})^2 \] 4. **Calculate Each Term**: - The first term \( (0 \, \text{m/s}) \cdot (5 \, \text{s}) = 0 \, \text{m} \). - The second term: \[ \frac{1}{2} (3 \, \text{m/s}^2) (5 \, \text{s})^2 = \frac{1}{2} (3) (25) = \frac{75}{2} = 37.5 \, \text{m} \] 5. **Combine the Results**: Since the first term is zero, the total distance \( s \) is: \[ s = 0 + 37.5 \, \text{m} = 37.5 \, \text{m} \] ### Conclusion The distance traveled by the car in the first 5 seconds is **37.5 meters**. However, since this value does not match any of the provided options, it seems there may have been a misunderstanding in the options or the question itself. ### Analyzing the Options - **A. 15 meters**: This is incorrect because it underestimates the distance based on the given acceleration and time. - **B. 30 meters**: This is also incorrect; it is still less than the calculated distance. - **C. 45 meters**: This is incorrect; it is slightly higher than the calculated distance. - **D. 75 meters**: This is incorrect; it significantly overestimates the distance. ### Common Pitfalls - **Misunderstanding the initial conditions**: Always ensure you correctly identify the initial velocity, especially if the object starts from rest. - **Forgetting to square the time**: In the equation \( \frac{1}{2} a t^2 \), the time must be squared, which is a common mistake. - **Not using the correct units**: Ensure that all units are consistent (e.g., meters, seconds). ### Revision Summary - Use the equation of motion \( s = ut + \frac{1}{2} a t^2 \) to find distance. - Substitute the correct values for initial velocity, acceleration, and time. - Calculate each term carefully, especially squaring the time. - Check your final answer against the options provided, and be aware of potential discrepancies.