The initial momentum of the system is:
$$P_i = m_1v_1 + m_2v_2$$
where:
$$m_1$$ is the mass of the first car (1250 kg)
$$v_1$$ is the velocity of the first car (32.0 m/s)
$$m_2$$ is the mass of the second car (875 kg)
$$v_2$$ is the velocity of the second car (0 m/s, since it is initially parked)
The final momentum of the system is:
$$P_f = (m_1 + m_2)v_f$$
where:
$$v_f$$ is the final velocity of the two cars, which we want to find
Setting the initial momentum equal to the final momentum, we get:
$$m_1v_1 + m_2v_2 = (m_1 + m_2)v_f$$
Solving for $$v_f$$, we get:
$$v_f = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$$
Substituting the given values, we get:
$$v_f = \frac{(1250 \text{ kg})(32.0 \text{ m/s}) + (875 \text{ kg})(0 \text{ m/s})}{1250 \text{ kg} + 875 \text{ kg}}$$
$$v_f = \frac{40000 \text{ kg m/s}}{2125 \text{ kg}}$$
$$v_f = 18.8 m/s$$
Therefore, the two cars move away at a velocity of 18.8 m/s.
