Question

If the velocity of an object doubles, then how does its kinetic energy change?

Answer 1

Step 1- Let velocity of an object= v m/s
Let mass of an object= m
Step 2- The kinetic energy of an object with mass m and velocity v is given by-
$K.E=\frac{m{v}^2}{2}$--------------------(I)
Step 3- Let's v' is the increased velocity and KE' is the kinetic energy of an object.
$K.E\text{'}=\frac{m{(v\text{'})}^2}{2}$-----------------(II)
According to the given question- v'=2v m/s
Substituting the value of v' in equation (II)
$$\begin{gathered} K.E\text{'}=\frac{m{\left(2v\right)}^2}{2} \\ K.E\text{'}=\frac{4m{v}^2}{2} \\ K.E\text{'}=4(K.E)----U\sin gequation\left(I\right) \end{gathered}$$

Hence kinetic energy of an object will become four-time if the velocity of an object doubles.