Which object has the greatest kinetic energy?

To determine which object has the greatest kinetic energy, it's essential to apply the formula for kinetic energy, which is given by:

[ KE = \frac{1}{2}mv^2 ]

where ( m ) is the mass of the object and ( v ) is its speed.

For the first choice, with mass ( 2m ) and speed ( 3v ), the kinetic energy can be calculated as follows:

[ KE_A = \frac{1}{2}(2m)(3v)^2 = \frac{1}{2}(2m)(9v^2) = 9mv^2 ]

For the second choice, with mass ( m ) and speed ( v ), the kinetic energy is:

[ KE_B = \frac{1}{2}m(v)^2 = \frac{1}{2}mv^2 ]

For the third choice, with mass ( m ) and speed ( 3v ):

[ KE_C = \frac{1}{2}m(3v)^2 = \frac{1}{2}m(9v^2) = \frac{9}{2}mv^2 ]

For the fourth