Question

how fast is the collision crash of a 5,000kg car moving with a velocity of 5.2 m/s that hits a stationary 8,000kg truck on a frictionless track

Answer 1

Assuming that the collision is purely inelastic, we can apply conservation of momentum:

$$m_cv_c+m_tv_t=(m_t+m_c)u,\\\space\\ u=\frac{m_cv_c+m_tv_t}{m_t+m_c}=\frac{5000\cdot5.2+8000\cdot0}{5000+8000}=2\text{ m/s}.$$