The kinetic energy of an object is given by the formula KE = 1/2 mv^2, where m is the mass and v is the velocity. Since both objects have equal mass, the kinetic energies will be directly related to the square of their speeds.

For object x, the kinetic energy is kx = 1/2 m(u^2). For object y, with a speed of 3u, the kinetic energy is ky = 1/2 m(3u)^2 = 1/2 m(9u^2) = 9kx.

Option 1 (kx = ky) and Option 2 (2kx = ky) are incorrect because they suggest that the kinetic energies are equivalent or directly proportional to the speeds, however, kinetic energy is dependent on the square of speed.

Option 4 (3kx = ky) is incorrect because it suggests that the kinetic energy of y is three times that of x, but since y`s speed is 3u, its kinetic energy is nine (not three) times greater, as speed is squared in the calculation of kinetic energy.

Hence, the correct answer is option 3 (9kx = ky), which accurately represents the relationship given y`s speed