Particles with the same velocity can have different kinetic energies if they have different masses. Kinetic energy is a measure of the energy possessed by an object due to its motion, and it depends on both the mass and velocity of the object.
The formula for kinetic energy (KE) is:
KE = (1/2) * m * v^2
where m represents the mass of the object and v represents its velocity.
As you can see from the formula, kinetic energy is directly proportional to the square of the velocity and the mass of the object. This means that even if two particles have the same velocity, their kinetic energies can differ if their masses are different.
For example, consider two particles, A and B, both moving with a velocity of 10 meters per second. If particle A has a mass of 2 kilograms and particle B has a mass of 5 kilograms, their kinetic energies will be different. The kinetic energy of particle A would be:
KE_A = (1/2) * 2 kg * (10 m/s)^2 = 100 Joules
while the kinetic energy of particle B would be:
KE_B = (1/2) * 5 kg * (10 m/s)^2 = 250 Joules
Even though they have the same velocity, particle B has a higher kinetic energy because it has a greater mass.
This illustrates that kinetic energy depends on both the velocity and the mass of an object. Two particles with the same velocity will have the same kinetic energy only if they also have the same mass.