Calculate the kinetic energies and decide which is the greatest ? a) mass of 4m and velocity v b) mass of 3m velocity 2v c) mass 2m velocity 3v...

We'll have to recall the kinetic energy
equation:

K.E. = mass*squared
velocity/2

K.E. = m*v^2/2

Now,
we'll have to plug the given data into the equation above and then we'll decide which is
the greatest.

For the object that has the mass 4m and the
velocity v, we'll get:

K.E. =
4m*v^2/2

K.E. = 2m*v^2

For the
object that has the mass 3m and the velocity 2v, we'll
get:

K.E. = 3m*4v^2/2

K.E. =
6m*v^2

For the object that has the mass 2m and the velocity
3v, we'll get:

K.E. =
2m*9v^2/2

K.E. = 9m*v^2

For
the object that has the mass m and the velocity 4v, we'll
get:

K.E. = m*16v^2/2

K.E. =
8m*v^2

We notice that the object that has the
mass 2m and the velocity 3v has the greatest kinetic energy, therefore the correct
option is c).