# 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 d) mass m velocity 4v

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We'll recall the kinetic energy equation:

K.E. = mass*squared velocity/2

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

Now, we'll calculate the kinetic energy for each object:

a) K.E. = 4m*v^2/2 => K.E. = 2m*v^2

b) K.E. = 3m*4v^2/2 => K.E. = 6m*v^2

c) K.E. = 2m*9v^2/2 => K.E. = 9m*v^2

d) K.E. = m*16v^2/2 => K.E. = 8m*v^2

**It is obvious that the object that has the gretest kinetic energy is the one whose features are 2m and 3v, therefore the correct option is c) K.E. = 9m*v^2.**

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).**