For a fixed mass, if the speed of a ball is halved, what will be its kinetic energy?

If the speed of a ball is halved, its kinetic energy will be reduced to one-fourth of its original value. This is because kinetic energy is directly proportional to the square of the velocity.

Mathematically, the kinetic energy (KE) of an object is given by the formula:

KE = 0.5 * m * v^2

Where:
KE = Kinetic energy
m = Mass of the object
v = Velocity of the object

If the speed of the ball is halved, the new velocity (v') will be half of the original velocity (v). Therefore, the new kinetic energy (KE') will be:

KE' = 0.5 * m * (0.5v)^2
KE' = 0.5 * m * (0.25v^2)
KE' = 0.125 * m * v^2

Therefore, the new kinetic energy (KE') will be one-fourth (0.125) of the original kinetic energy (KE).

Kinetic energy, KE = 1/2 - mass - (speed)^2

If mass is fixed and speed is halved, then new speed = 1/2 - initial speed

Therefore, KE = 1/2 - mass - (1/2 - initial speed)^2
= 1/2 - mass - 1/4 - (initial speed)^2
= 1/8 - mass - (initial speed)^2

Therefore, kinetic energy becomes 1/8 times of its initial value.