The electric motor of a model train accelerates the train from rest to 0.640 m/s in 19.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.
power= work/time= 1/2 m vf^2 / time
thank You
To find the average power delivered to the train during its acceleration, we can use the formula:
Power (P) = Work (W) / Time (t)
Since the work done on an object is equal to the change in kinetic energy, we can rewrite the formula as:
P = ΔKE / t
The change in kinetic energy (ΔKE) can be calculated using the equation:
ΔKE = 1/2 * m * (vf^2 - vi^2)
Where:
- m is the mass of the train
- vf is the final velocity (0.640 m/s)
- vi is the initial velocity (0 m/s, since the train starts from rest)
First, convert the mass of the train from grams to kilograms:
m = 875 g / 1000 = 0.875 kg
Next, calculate the change in kinetic energy:
ΔKE = 1/2 * 0.875 kg * (0.640 m/s)^2
ΔKE = 0.5 * 0.875 kg * (0.640 m/s)^2
ΔKE = 0.5 * 0.875 kg * 0.4096 m^2/s^2
ΔKE = 0.1792 J
Now, we can calculate the average power using the formula:
P = ΔKE / t
Convert the time from milliseconds to seconds:
t = 19.0 ms / 1000 = 0.019 s
P = 0.1792 J / 0.019 s
P ≈ 9.42 W
Therefore, the average power delivered to the train during its acceleration is approximately 9.42 Watts.