Question

A particle of m has a velocity of vxˆi+vyˆj+vzˆk. Is its kinetic energy given by m(vx^2ˆi+vy^2ˆj+vz^2ˆk)/2? If not, what is the correct expression?

a) Yes; the expression is correct
b) No; the correct expression is (m/2)(vx^2+vy^2+vz^2)
c) No; the correct expression is m(vx^2+vy^2+vz^2)/2
d) Depends on the direction of the velocity components

Answer 1

The correct expression for the kinetic energy of a particle with velocity vxˆi+vyˆj+vzˆk and mass m is m(vx^2+vy^2+vz^2)/2.

Step-by-step explanation:

The correct expression for the kinetic energy of a particle with velocity vxˆi+vyˆj+vzˆk and mass m is m(vx^2+vy^2+vz^2)/2. This is because the kinetic energy is given by half the product of the mass and the square of the speed. In this case, the speed is represented by the magnitude of the velocity vector, which is vx^2+vy^2+vz^2.