Respuesta :
We are asked about the kinetic energy of an object. The kinetic energy is given by the following formula:
[tex]E_k=\frac{1}{2}mv^2[/tex]Where:
[tex]\begin{gathered} m=\text{ mass} \\ v=\text{ velocity} \end{gathered}[/tex]Part a) If the velocity is multiplied by 3 we have:
[tex]E_k=\frac{1}{2}m(3v)^2[/tex]Solving the square we get:
[tex]E_k=\frac{1}{2}m9v^2[/tex]Factoring out the 4 we get:
[tex]E_k=9(\frac{1}{2}mv^2)[/tex]Therefore, the kinetic energy is multiplied by 9.
Part b) If the kinetic energy is multiplied by 4 we have in the formula:
[tex]E_k=4(\frac{1}{2}mv^2)[/tex]We can move the 4 next to the velocity:
[tex]E_k=\frac{1}{2}m4v^2[/tex]Now, by properties of exponents, we can rewrite the formula as:
[tex]E_k=\frac{1}{2}m(2v)^2[/tex]Therefore, the velocity is multiplied by 2.
Part c can be solved using the same procedure as in par b.
