First, calculate the acceleration of the car and trailer.
$$F = ma$$
$$F = (m_c + m_t)a$$
where F is the force acting on the car and trailer, m_c is the mass of the car, m_t is the mass of the trailer, and a is the acceleration.
We know that the force acting on the car and trailer is the force of friction between the tires and the road.
$$F = \mu_k m_c g$$
where \mu_k is the coefficient of kinetic friction between the tires and the road and g is the acceleration due to gravity.
We also know that the acceleration of the car and trailer is:
$$a = \frac{v_f^2 - v_i^2}{2d}$$
where v_f is the final velocity of the car and trailer (0 m/s), v_i is the initial velocity of the car and trailer, and d is the distance the car and trailer skids (25 m).
Substituting the expressions for F and a into the equation $$F = ma$$, we get:
$$\mu_k m_c g = (m_c + m_t)\left(\frac{v_f^2 - v_i^2}{2d}\right)$$
Solving this equation for v_i, we get:
$$v_i = \sqrt{2\mu_k gd + \frac{\mu_k m_t g}{m_c}d}$$
Plugging in the given values (m_c = 1000 kg, m_t = 2000 kg, \mu_k = 0.5, d = 25 m), we get:
$$v_i = \sqrt{2(0.5)(9.8 m/s^2)(25 m) + \frac{(0.5)(2000 kg)(9.8 m/s^2)(25 m)}{1000 kg}}$$
$$v_i = 5 m/s$$
