A car of mass M traveling with velocity v strikes a car of mass M that is at rest. The two cars’ bodies mesh in the collision. The loss of the kinetic energy the moving car undergo in the collision is a) a quarter of the initial kinetic energy.
b) half of the initial kinetic energy.
c) all the initial kinetic energy.
d) zero.

the correct answer is B

Explanation:

Let's propose the solution of the problem, for this we form a system formed by the two cars, so that the forces during the collision are internal, the momentum is conserved

instantly starts. Before the crash

         p₀ = M v +0

final instant. After the crash

        m_f = (M + M) v_f

the moment is preserved

        p₀ = p_f

        M v = 2 M v_f

        v_f = v / 2

let's look for kinetic energy

before the crash

       K₀ = ½ M v²

after the crash

       K_f = ½ 2M (v_f)²

       K_f = ½ 2M (v/2)²

       K_f = (½ M v²) ½

       K_f = K₀ / 2

therefore the correct answer is B

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there are no contact forces mentioned on the list of choices that you've provided.