The law of conservation of momentum states that the total momentum of a closed system remains constant. In this case, the system consists of the blue car and the red car.
Before the collision, the momentum of the blue car can be calculated as:
p_blue = m_blue * v_blue
p_blue = 600 kg * 5 m/s
p_blue = 3000 kg·m/s
Since the red car is initially at rest, its momentum is zero:
p_red = m_red * v_red
p_red = 0
The total momentum of the system before the collision is therefore:
p_total = p_blue + p_red
p_total = 3000 kg·m/s + 0
p_total = 3000 kg·m/s
After the collision, the two cars stick together and move together as a single object. The final velocity of the combined object can be calculated using the law of conservation of momentum:
p_total = (m_blue + m_red) * v_final
Since the two cars stick together, their masses are added:
m_total = m_blue + m_red
m_total = 600 kg + 400 kg
m_total = 1000 kg
Solving for v_final, we get:
v_final = p_total / m_total
v_final = 3000 kg·m/s / 1000 kg
v_final = 3 m/s
Therefore, after the collision, the combined object (which is now the blue car and the red car stuck together) is moving at a velocity of 3 m/s.
To answer the question, we only need to calculate the initial momentum of the red car before the collision. As we saw earlier, the momentum of the red car before the collision was zero:
p_red = 0
Therefore, the initial momentum of the red car before the collision was zero.