Final answer:
The kinetic energy of a body is given by the equation K.E. = ½mv². When the velocity of a body is doubled, its kinetic energy becomes 4k, where k is the original kinetic energy.
Step-by-step explanation:
The kinetic energy of a body is given by the equation K.E. = ½mv², where K.E. represents the kinetic energy, m represents the mass of the body, and v represents the velocity of the body.
If the magnitude of the kinetic energy of a body is 'k' and its velocity is doubled, we can calculate the new kinetic energy using the formula:
K.E.₂ = ½m(v₂)²
Since the velocity is doubled, we substitute v₂ = 2v into the formula:
K.E.₂ = ½m(2v)² = 4(1)k = 4k
Therefore, the kinetic energy of the body when its velocity is doubled is 4k.