To determine the power of a motor, we need to use the formula for power, which is given by:
[tex]\[
P = \frac{E}{t}
\][/tex]
Here:
- [tex]\( P \)[/tex] is the power.
- [tex]\( E \)[/tex] is the energy transferred.
- [tex]\( t \)[/tex] is the time taken.
1. Identify the given values:
- Energy transferred: [tex]\( E = 10 \, \text{kJ} \)[/tex]
- Time taken: [tex]\( t = 25 \, \text{s} \)[/tex]
2. Convert the energy into the standard unit of Joules (J):
- [tex]\( 1 \, \text{kJ} = 1000 \, \text{J} \)[/tex]
Therefore,
[tex]\[ E = 10 \, \text{kJ} \times 1000 \, \text{J/kJ} = 10000 \, \text{J} \][/tex]
3. Substitute the values into the formula:
[tex]\[
P = \frac{E}{t} = \frac{10000 \, \text{J}}{25 \, \text{s}}
\][/tex]
4. Calculate the power:
[tex]\[
P = \frac{10000 \, \text{J}}{25 \, \text{s}} = 400 \, \text{W}
\][/tex]
Therefore, the power of the motor is [tex]\( 400 \, \text{W} \)[/tex].
