Question

A man has a box of weight \[10\,{\text{kg}}\] . The energy of the box, when the man runs with a constant velocity of \[2\,{\text{m/s}}\] along with the box behind the bus, is:
A. \[10\,{\text{J}}\]
B. \[30\,{\text{J}}\]
C. \[20\,{\text{J}}\]
D. \[2\,{\text{J}}\]

Answer 1

Hint: First of all, we will find the expression of kinetic energy, then substitute the required values and then manipulate accordingly.

Complete step by step answer:
In the given question, we are supplied,
Weight of the box is \[10\,{\text{kg}}\].
The velocity with which the man runs is \[2\,{\text{m/s}}\] .
The velocity mentioned in this case is constant in nature i.e. it has no acceleration in it.

When the man runs with the box, the work done by the man is converted into kinetic energy for both the man and box. However, we are only asked to calculate the kinetic energy of the box. The kinetic energy will remain associated with the box until the box comes to rest.

The kinetic energy is given by the formula as given below:
\[K.E = \dfrac{1}{2}m{v^2}\] …… (1)
Where,
\[K.E\] indicates the kinetic energy.
\[m\] indicates the mass of the box.
\[v\] indicates the velocity at which the box is moving.

Now, substituting the required values in the equation (1), we get:
  K.E = $ \dfrac{1}{2}m{v^2} \\ $
  K.E = $ \dfrac{1}{2} \times 10 \times {2^2}\,{\text{J}} \\ $
  K.E = $ 5 \times 4\,{\text{J}} \\ $
  K.E = $ 20\,{\text{J}} \\ $
Hence, the required energy associated with the box is \[20\,{\text{J}}\] .

So, the correct answer is “Option C”.

Additional Information:
In mechanics, an object's kinetic energy is the energy it possesses due to its motion. It is defined as the work required to accelerate from rest to the specified velocity of a body of a given mass. Having accumulated this energy through its acceleration, once its speed increases, the body retains this kinetic energy until the speed changes.

Note:
The kinetic energy directly depends on the mass of the body and velocity with which it is moving. Higher the velocity or larger the mass is, greater is its kinetic energy. It does not depend on final and initial position.