To determine the power developed in the engine of the car, we need to follow a series of steps involving the concepts of work, energy, and power in physics. Let's break it down step-by-step. ### Step 1: Calculate the Kinetic Energy (KE) of the Car The kinetic energy of an object can be calculated using the formula: \[ KE = \frac{1}{2} mv^2 \] where: - \( m \) is the mass of the object (in kilograms), - \( v \) is the velocity of the object (in meters per second). For the car: - Mass \( m = 800 \, \text{kg} \) - Speed \( v = 25 \, \text{m/s} \) Substituting the values into the formula: \[ KE = \frac{1}{2} \times 800 \, \text{kg} \times (25 \, \text{m/s})^2 \] Calculating \( (25 \, \text{m/s})^2 \): \[ (25 \, \text{m/s})^2 = 625 \, \text{m}^2/\text{s}^2 \] Now substituting back into the kinetic energy formula: \[ KE = \frac{1}{2} \times 800 \times 625 \] \[ KE = 400 \times 625 = 250000 \, \text{J} \quad (\text{Joules}) \] ### Step 2: Calculate the Power Developed Power is defined as the rate at which work is done or energy is transferred. The formula for power \( P \) is: \[ P = \frac{W}{t} \] where: - \( W \) is the work done (or energy transferred, in this case, the kinetic energy), - \( t \) is the time taken (in seconds). From our previous calculation, we found that the work done (or kinetic energy) is \( 250000 \, \text{J} \), and the time taken to reach this speed is \( 20 \, \text{s} \). Substituting these values into the power formula: \[ P = \frac{250000 \, \text{J}}{20 \, \text{s}} = 12500 \, \text{W} \] ### Step 3: Convert Power to Kilowatts Since power is often expressed in kilowatts (kW), we can convert watts to kilowatts by dividing by 1000: \[ P = \frac{12500 \, \text{W}}{1000} = 12.5 \, \text{kW} \] ### Step 4: Final Answer in Watts To express this in standard form, we can write: \[ P = 1.25 \times 10^4 \, \text{W} \] ### Conclusion: Correct Option The correct option is **A. 1.25 x 10^4 W**. ### Explanation of Other Options - **B. 2.50 x 10^4 W**: This value is too high. It would imply that the car developed more power than calculated, which is not supported by the energy and time values given. - **C. 1.25 x 10^6 W**: This is an order of magnitude too high. It suggests a power level that is unrealistic for a typical car engine in this scenario. - **D. 2.50 x 10^6 W**: This is also significantly too high and would imply an extremely powerful engine, far beyond typical automotive applications. ### Revision Summary - Kinetic energy is calculated using \( KE = \frac{1}{2} mv^2 \). - Power is the rate of doing work, calculated as \( P = \frac{W}{t} \). - The car's kinetic energy was found to be 250,000 J, leading to a power output of 12,500 W or 1.25 x 10^4 W. - Always check units and conversions when calculating power and energy.