Part A Select the correct equations that show that a 2500000 -J change in kinetic energy occurs for an airplane that is moved 500 m in takeoff by a sustained force of 5000 N . W \( =F^{2} / g=(5000 \mathrm{~N})^{2} /(10 \mathrm{~N} / \mathrm{m})=2500000 \mathrm{~J} \) \( W=F d / g=(5000 \mathrm{~N})(500 \mathrm{~m}) /(10 \mathrm{~N} / \mathrm{m})=2500000 \mathrm{~J} \) \( W=F d=(5000 \mathrm{~N})(500 \mathrm{~m})=2500000 \mathrm{~J} \) \( W=d^{2} g=(500 \mathrm{~m})^{2}(10 \mathrm{~N} / \mathrm{m})=2500000 \mathrm{~J} \) Submit Request Answer

To determine which equations correctly show that a 2,500,000 J change in kinetic energy occurs for the airplane, we need to analyze the work done by the force during the takeoff. The work done \( W \) by a constant force \( F \) over a distance \( d \) is given by the formula: \[ W = F \cdot d \] Given: - \( F = 5000 \, \text{N} \) - \( d = 500 \, \text{m} \) Now, let's calculate the work done using the correct formula: \[ W = (5000 \, \text{N})(500 \, \text{m}) = 2500000 \, \text{J} \] Now, let's evaluate each of the provided equations: 1. **\( W = \frac{F^2}{g} = \frac{(5000 \, \text{N})^2}{(10 \, \text{N/m})} \)** This equation is incorrect because it does not represent the work done in the context of force and distance. 2. **\( W = \frac{F d}{g} = \frac{(5000 \, \text{N})(500 \, \text{m})}{(10 \, \text{N/m})} \)** This equation is also incorrect because it incorrectly divides the work by \( g \), which is not applicable in this context. 3. **\( W = F d = (5000 \, \text{N})(500 \, \text{m}) \)** This equation is correct and matches our calculation, yielding \( W = 2500000 \, \text{J} \). 4. **\( W = d^2 g = (500 \, \text{m})^2 (10 \, \text{N/m}) \)** This equation is incorrect because it does not represent the work done by the force in the context of the problem. ### Conclusion: The correct equation that shows a 2,500,000 J change in kinetic energy is: - **\( W = F d = (5000 \, \text{N})(500 \, \text{m}) = 2500000 \, \text{J} \)** This is the only valid equation among the options provided.