The statement "the kinetic energy of a particle is equal to the square of its velocity" is not accurate. The kinetic energy of a particle is actually proportional to the square of its velocity, not equal to it.
The correct relationship between kinetic energy (KE) and velocity (v) is given by the following equation:
KE = (1/2)mv^2
Where: KE is the kinetic energy of the particle, m is the mass of the particle, v is the velocity of the particle.
This equation shows that the kinetic energy is directly proportional to the square of the velocity. When the velocity of a particle doubles, its kinetic energy increases by a factor of four (2^2 = 4). Similarly, when the velocity triples, the kinetic energy increases by a factor of nine (3^2 = 9).
In other words, if you compare two particles with the same mass, the one with a higher velocity will have a greater kinetic energy. The relationship between kinetic energy and velocity highlights the significance of velocity in determining the amount of energy associated with the motion of an object.
It's important to note that this equation holds true only for non-relativistic speeds, where the particle's velocity is significantly less than the speed of light. At speeds close to or approaching the speed of light, relativistic effects come into play, and the relationship between kinetic energy and velocity becomes more complex, involving the concept of relativistic mass and energy.