What is the final velocity of two cars, one weighing 1,450 kg moving at 25.0 m/s and the other stationary at 1,550 kg, after they collide and lock bumpers?

To find the final velocity of the two cars after they collide and lock bumpers, we can apply the principle of conservation of momentum. This states that the total momentum before the collision must equal the total momentum after the collision, provided no external forces act on the system.

First, we calculate the initial momentum of both cars. The momentum of the first car (1,450 kg moving at 25.0 m/s) is given by:

[

p_1 = m_1 \cdot v_1 = 1450 , \text{kg} \cdot 25.0 , \text{m/s} = 36,250 , \text{kg m/s}

]

The second car, which is stationary, has an initial momentum of zero:

[

p_2 = m_2 \cdot v_2 = 1550 , \text{kg} \cdot 0 , \text{m/s} = 0 , \text{kg m/s}

]

Thus, the total initial momentum of the system is:

[

p_{\text{initial}} = p_1 + p_2 = 36,250 , \text