A force applied by an engine of a train of mass 2.05 x 10^6 kg changes its velocity from 5m/s to 25m/s in 5 minutes. The power of the engine is:

Explanation

To calculate the power of the engine, we need to use the equation: Power = Force × Velocity First, let's calculate the force applied by the engine. We can use Newton's second law of motion, which states: Force = Mass × Acceleration Given that the mass of the train is 2.05 × 106 kg and the change in velocity is from 5 m/s to 25 m/s, we can calculate the acceleration using the equation: Acceleration = (Change in Velocity) / Time The change in velocity is 25 m/s - 5 m/s = 20 m/s. The time given is 5 minutes, but we need to convert it to seconds. There are 60 seconds in a minute, so 5 minutes is equal to 5 × 60 = 300 seconds. Therefore, the acceleration is: Acceleration = (20 m/s) / (300 s) = 0.0667 m/s² Now we can calculate the force: Force = (Mass) × (Acceleration) = (2.05 × 106 kg) × (0.0667 m/s²) = 136,835 N Finally, we can calculate the power: Power = (Force) × (Velocity) = (136,835 N) × (25 m/s) = 3,420,875 W Therefore, the power of the engine is 3,420,875 Watts (W). To convert the power from watts to megawatts, we divide the power value by one million (106) since there are one million watts in a megawatt. Power in megawatts (MW) = Power in watts (W) / 106 In this case, the power of the engine is: Power = 3,420,875 W / 10^6 = 3.420875 MW