Answer :
Answer:
The kinetic energy increases by a factor of 9
Explanation:
Kinetic Energy
It's the energy related to the speed of an object and is calculated by the formula
[tex]\displaystyle K=\frac{mv^2}{2}[/tex]
Let's suppose the initial speed of the mass is [tex]v_o[/tex], then the kinetic energy is
[tex]\displaystyle K_o=\frac{mv_o^2}{2}[/tex]
Now the speed will triple, i.e. [tex]v_1=3v_o[/tex]. The new kinetic energy is
[tex]\displaystyle K_1=\frac{mv_1^2}{2}[/tex]
[tex]\displaystyle K_1=\frac{m(3v_o)^2}{2}[/tex]
[tex]\displaystyle K_1=9\frac{mv_o^2}{2}[/tex]
Thus
[tex]K_1=9K_o[/tex]
The kinetic energy increases by a factor of 9
Let's check with numbers: [tex]v_o=20,\ v_1=60[/tex]
[tex]\displaystyle K_o=\frac{m20^2}{2}=200m[/tex]
[tex]\displaystyle K_1=\frac{m60^2}{2}=1800m[/tex]
The relation is
[tex]\displaystyle \frac{K_1}{K_o}=9[/tex]
The new kinetic energy is nine times the initial kinetic energy.