Answer:
100 J, 225 J
Explanation:
The kinetic energy of an object is given by:
![K=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=K%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where
m is the mass of the object
v is the velocity of the object
In this problem, the initial kinetic energy of the object is
K = 25 J
Then, the velocity is doubled, which means
v' = 2v
Therefore, the new kinetic energy will be
![K'=\frac{1}{2}m(2v)^2 = 4(\frac{1}{2}mv^2)=4K](https://tex.z-dn.net/?f=K%27%3D%5Cfrac%7B1%7D%7B2%7Dm%282v%29%5E2%20%3D%204%28%5Cfrac%7B1%7D%7B2%7Dmv%5E2%29%3D4K)
Therefore, the kinetic energy has quadrupled:
![K' = 4(25)=100 J](https://tex.z-dn.net/?f=K%27%20%3D%204%2825%29%3D100%20J)
Later, the velocity is tripled, which means
v'' = 3v
Therefore, the new kinetic energy will be
![K''=\frac{1}{2}m(3v)^2 = 9(\frac{1}{2}mv^2)=9K](https://tex.z-dn.net/?f=K%27%27%3D%5Cfrac%7B1%7D%7B2%7Dm%283v%29%5E2%20%3D%209%28%5Cfrac%7B1%7D%7B2%7Dmv%5E2%29%3D9K)
Therefore, the kinetic energy has increased by a factor of 9:
![K' = 9(25)=225 J](https://tex.z-dn.net/?f=K%27%20%3D%209%2825%29%3D225%20J)