Final answer:
Increasing the speed of a body by 4 times will result in an increase of the body's kinetic energy by a factor of 16, due to the square relationship between speed and kinetic energy.
Step-by-step explanation:
If the speed of a body is increased 4 times, the kinetic energy would be affected significantly since kinetic energy is directly proportional to the square of speed. According to the formula for kinetic energy, KE = 1/2 m v^2, where m is the mass and v is the velocity of the object, if the speed is quadrupled, the kinetic energy will increase by a factor of the speed squared. Therefore, increasing the speed by a factor of 4 would result in the kinetic energy increasing by 4^2, which is 16 times.