The electric motor of a model train accelerates the train from rest to 0.755 m/s in 19.5 ms. The total mass of the train is 875 g. Find the average power delivered to the train during the acceleration.
To find the average power delivered to the train during acceleration, we can use the formula:
Power = work / time
To calculate the work done during the acceleration, we can use the formula:
Work = force × distance
First, let's find the force acting on the train using Newton's second law of motion:
Force = mass × acceleration
Given mass m = 875 g = 0.875 kg
Acceleration a = change in velocity / time taken
= (0.755 m/s - 0 m/s) / (19.5 ms)
= 0.755 m/s / 0.0195 s
≈ 38.72 m/s^2
Substituting these values into the equation:
Force = 0.875 kg × 38.72 m/s^2
≈ 33.83 N
Now, we can calculate the work done during the acceleration:
Distance = 0.5 × (initial velocity + final velocity) × time taken
= 0.5 × (0 m/s + 0.755 m/s) × 0.0195 s
≈ 0.007335 m
Work = Force × Distance
= 33.83 N × 0.007335 m
≈ 0.248 J
Finally, we can calculate the average power delivered to the train during the acceleration:
Power = Work / Time
= 0.248 J / 0.0195 s
≈ 12.72 W
Therefore, the average power delivered to the train during the acceleration is approximately 12.72 watts.