Question

when two objects collide and stick together, what happens to their speed, assuming the momentum is conserved?

answer options:
select one of four

the objects will move at the same velocity as before the collision.
the objects will slow down after they collide.
the objects will slow down for an instant before speeding back up.
the objects will speed up after they collide.

Explanation:

This is a perfectly inelastic collision (objects stick together). By the law of conservation of momentum, \( m_1v_1 + m_2v_2=(m_1 + m_2)v_f \), so \( v_f=\frac{m_1v_1 + m_2v_2}{m_1 + m_2} \). The total mass after collision (\( m_1 + m_2 \)) is greater than either individual mass before. If we consider typical cases (e.g., two objects moving towards each other or one moving and one stationary), the final velocity \( v_f \) will be less than the initial velocities of the objects (or a weighted average that results in a lower speed when mass increases). So the objects slow down after collision.

Answer:

The objects will slow down after they collide.