Answer:
[tex]t_2=\sqrt{2}(t_1)[/tex]
Explanation:
The kinetic energy of a body is that energy it possesses due to its motion. In classical mechanics, this energy depends only on its mass and speed, as follows:
[tex]K=\frac{mv^2}{2}[/tex]
The speed in an uniformly accelerated motion is given by:
[tex]v=at[/tex]
Replacing this expression in the formula for the kinetic energy, we have:
[tex]K=\frac{ma^2t^2}{2}\\[/tex]
So, if we have [tex]K_2=2K_1[/tex]:
[tex]K_1=\frac{ma^2t_1^2}{2}(1)\\K_2=\frac{ma^2t_2^2}{2}\\2K_1=\frac{ma^2t_2^2}{2}\\K_1=\frac{ma^2t_2^2}{4}(2)\\[/tex]
Equaling (1) and (2) and solving for [tex]t_2[/tex]:
[tex]\frac{ma^2t_1^2}{2}=\frac{ma^2t_2^2}{4}\\t_2=\frac{4t_1^2}{2}\\t_2=\sqrt{2t_1^2}\\t_2=\sqrt{2}(t_1)[/tex]
