I have a physics/pre-calculus question...I think it's fairly easy if you know your stuff.?

Question

The kinetic energy E(sub k) of a moving object, measured in joules, varies jointly as the mass "m" of the object and the square of speed "v". Find the constant of variation "k" if E(sub K) is 36 joules, "m" is 4.5 kilograms and "v" is 4 meters per second.

Answer 1

KE = f(m, v) = k ( m ) ( v^2 )

36 J = k ( 4.5 kg ) ( 4 m/s )^2

36 / ( ( 4.5 ) ( 4^2 ) ) = k

1/2 = k

So we arrive at the familiar expression

KE = 1/2 m v^2

as expected

Answer 2

E_K = kmv², for some constant of variation k.

E_K = 36 J, m = 4.5 kg, v = 4 m/s

36 = k(4.5)(4)²
36 = k(4.5)(16)
36 = k(72)
36/72 = k
k = 1/2

E_K = (1/2)mv²