Two bodies of different masses are acted upon by the same force for the same time. They will acquire the same:

Question

A body of mass 2 kg is moving with a velocity of 3 m/s. What is its kinetic energy?

Answer 1

Use the impulse-momentum relation directly instead of comparing velocities.

Impulse is given by $J = F \times t$, and since $F$ and $t$ are the same for both bodies, the impulse $J$ delivered to each one is the same fixed number.
Impulse always equals the change in momentum produced, so starting from rest, $m_1 v_1 = J$ for the first body and $m_2 v_2 = J$ for the second body.
Since both equal the same $J$, it follows that $m_1 v_1 = m_2 v_2$, meaning the two bodies end up with equal momentum even though their masses $m_1$ and $m_2$ are different.
Because the masses differ, the individual velocities $v_1$ and $v_2$ work out to be different, and so do the accelerations and kinetic energies of the two bodies.

The one quantity guaranteed to match for both bodies is momentum, so option D is correct.

Answer 2

Use the impulse-momentum relation directly instead of comparing velocities.

Impulse is given by $J = F \times t$, and since $F$ and $t$ are the same for both bodies, the impulse $J$ delivered to each one is the same fixed number.
Impulse always equals the change in momentum produced, so starting from rest, $m_1 v_1 = J$ for the first body and $m_2 v_2 = J$ for the second body.
Since both equal the same $J$, it follows that $m_1 v_1 = m_2 v_2$, meaning the two bodies end up with equal momentum even though their masses $m_1$ and $m_2$ are different.
Because the masses differ, the individual velocities $v_1$ and $v_2$ work out to be different, and so do the accelerations and kinetic energies of the two bodies.

The one quantity guaranteed to match for both bodies is momentum, so option D is correct.

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