Question

The power output of a motor is $5{\text{kW}}$. What is the work done by the motor in $5s$.
A) $2.5{\text{kJ}}$.
B) $25{\text{kJ}}$.
C) $250{\text{kJ}}$.
D) $25000{\text{kJ}}$.

Answer 1

By using the formula of power output we can solve this problem as the formula of power output contains work done as well as time taken by motor. Power output is defined as the rate of change of doing work. Mathematically it is the ratio of work done and time taken, the work done can be present in Joules or Kilojoules but the time is always taken in seconds.

Formula: The formula for power output is given by, $P = \dfrac{w}{t}$ where $P$ is power output and $w$ is the work done and $t$ is time taken.

Step by step solution:
Step 1.
As given that the formula of the power output is equals to $P = \dfrac{w}{t}$ and also it is given that the value of power output is $5{\text{kW}}$ and the time taken is $5s$.

Step 2.
Let us put the given values in the formula of power output.
Since $P = \dfrac{w}{t}$
Replace the value of work done and time taken in the above formula.
$P{\text{ }} = {\text{ }}\dfrac{w}{t}$
Put $P = 5{\text{kW}}$ and $t = 5s$.
$P{\text{ }} = {\text{ }}\dfrac{w}{t} \\\ \Rightarrow 5 = \dfrac{w}{5} \\\ \Rightarrow w = 5 \times 5 \\\ \Rightarrow w = 25{\text{kJ}} \\\$
So, the work done by the motor is given by $w = 25{\text{kJ}}$

therefore option B is the correct answer for this problem.

Additional information: The definition of power is given by, it is the rate at which the work is done and mathematically it can be given by ${\text{Power = }}\dfrac{{{\text{work done}}}}{{{\text{time taken}}}}$ where work done can be in joules or kilojoules but the time taken is always in seconds the power can also be calculated as product of force and velocity with which the body is travelling, mathematically $P = F \cdot v$ where $F$ is force experienced and $v$ is the velocity with which the body is travelling.

Note: While solving such questions students should observe the options first and then convert the answer into the given options. Students should always remember the formula of power output because it is sometimes asked directly in problems and sometimes we require the formula for solving some problems indirectly.