Question

A $10kg$ object has $500J$ of kinetic energy because of its speed. How fast is the object traveling?

Answer 1

This question utilizes the Work – Energy theorem. We know that when an object possesses speed in any direction, it also possesses kinetic energy. Using the formula for determination of kinetic energy when mass and velocity are given, we can easily find the answer.

Formulae used :
$K.E. = \dfrac{1}{2}m{v^2}$ where $K.E.$ is the kinetic energy of the body, $m$ is the mass of the body and $v$ is the velocity of the body

Complete answer:
According to the given question,
Mass of the body ${m_b} = 10kg$
Kinetic energy possessed by the body $K.E. = 500J$
We know that
$\Rightarrow K.E. = \dfrac{1}{2}m{v^2}$
Substituting the respective values in their respective places, we get
$\Rightarrow 500J = \dfrac{1}{2} \times 10kg \times {v^2} \\\ \Rightarrow {v^2} \times 10kg \times \dfrac{1}{2} = 500J \\\ \Rightarrow {v^2} \times 5kg = 500J \\\ \Rightarrow {v^2} = \dfrac{{500}}{5}{\left( {m{s^{ - 1}}} \right)^2} \\\ \Rightarrow {v^2} = 100{\left( {m{s^{ - 1}}} \right)^2} \\\$
Now, using square root on both sides, we have
$\Rightarrow v = \sqrt {100{{\left( {m{s^{ - 1}}} \right)}^2}} \\\ \Rightarrow v = 10m{s^{ - 1}} \\\$
Therefore, the velocity of the object is $10m{s^{ - 1}}$.
Note: In the above question, we have used unit transformations. We know that Joule is newton metre and newton is kilogram metre per second square. Therefore, on dividing joule with kilogram, we are left with metre square per second square. This unit is actually velocity square. Thus, when we put a square root over it, the unit becomes that of velocity.