Help. Can someone provide a formula. ty The electric motor of a model train accelerates the train from rest to 0.540 m/s in 35.0 ms. The total mass of the train is 685 g. Find the average power delivered to the train during its acceleration.
Sure! To find the average power delivered to the train during its acceleration, we can use the equation:
\[ P = \frac{W}{\Delta t} \]
where P represents power, W represents work, and Δt represents the change in time.
To find the work done by the electric motor, we can use the equation:
\[ W = \frac{1}{2} \times m \times v^2 \]
where m represents the mass of the train and v represents the velocity.
First, we need to convert the mass of the train from grams to kilograms. There are 1000 grams in a kilogram, so:
\[ \text{mass} = \frac{685}{1000} = 0.685 \, \text{kg} \]
Next, we can plug in the values we have into the equation for work:
\[ W = \frac{1}{2} \times 0.685 \, \text{kg} \times (0.540 \, \text{m/s})^2 \]
Simplifying:
\[ W = \frac{1}{2} \times 0.685 \, \text{kg} \times 0.2916 \, \text{m}^2/\text{s}^2 \]
\[ W \approx 0.099 \, \text{J} \]
Now, we can calculate the average power by dividing the work by the change in time:
\[ P = \frac{0.099 \, \text{J}}{35.0 \, \text{ms}} \]
Since the time is given in milliseconds, we need to convert it to seconds. There are 1000 milliseconds in a second:
\[ P = \frac{0.099 \, \text{J}}{0.035 \, \text{s}} \]
Simplifying:
\[ P \approx 2.83 \, \text{W} \]
Therefore, the average power delivered to the train during its acceleration is approximately 2.83 Watts.