Question

How fast should a girl of 40 kg run so that her kinetic energy is 320 J.
(A) 64 m/s
(B) 8 m/s
(C) 16 m/s
(D) 4 m/s

Answer 1

We can use the relation between the mass of the object and its speed because it can give information about the kinetic energy of the moving object. The kinetic energy and mass of the girl is given in the question, so by the relation, we can determine the speed of the girl.

Complete step by step answer:
It is given that the mass of the girl is 40 kg and she is running with some speed. Due to this, the girl obtained some amount of kinetic energy and the magnitude of the kinetic energy obtained by the girl due to its motion is 320 J.
Let the speed of the girl is $v$.
Here use the expression of the kinetic energy of the girl for the calculation of its speed
$KE = \dfrac{1}{2}m{v^2}$
Here, $m$ is the mass of the girl and $KE$ is the kinetic energy of the girl.
Substitute the values of $m$ and $KE$ in the above equation.
Therefore we get,
$\begin{array}{l} 320 = \dfrac{1}{2} \times 40 \times {v^2}\\\ {v^2} = \dfrac{{640}}{{40}}\\\ {v^2} = 16\\\ v = 4\;{\rm{m/s}} \end{array}$
Hence, option (D) is correct, that is 4 m/s.

Note: The work done by the moving object can be obtained with the help of energy gained by the object, here work of the girl is running and her obtained energy is kinetic energy, So use this concept for the calculation of the correct answer from the given options.