Question 210688
A. Double the velocity:
{{{E = highlight_green((1/2)MV^2)}}} Substitute V = 2V
{{{E = (1/2)M(2V)^2}}} Simplify.
{{{E = (1/2)M*4V^2}}}
{{{E = highlight(4)highlight_green((1/2)MV^2)}}} As you can see, the energy is quadrupled when the velocity is doubled.  This makes sense when you see that the velociy, V, in the equation is squared, and 2 squared is 4.
B. Triple the velocity and triple the mass.
{{{E = highlight_green((1/2)MV^2)}}} Substitute V = 3V and M = 3M.
{{{E = (1/2)(3M)(3V)^2}}} Simplify.
{{{E = (1/2)(3M)(9V^2)}}}
{{{E = highlight(27)highlight_green((1/2)MV^2)}}} Here you can see that the energy is increased 27-fold.