Question

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

Explanation:

This is a perfectly inelastic collision (objects stick together). The formula for conservation of momentum is $m_1v_1 + m_2v_2=(m_1 + m_2)v_f$. After collision, the total mass ($m_1 + m_2$) is greater than either individual mass. Since momentum is conserved, if the total mass increases, the final velocity $v_f$ must be less than the initial velocities (assuming positive momenta). So the objects slow down. The other options are incorrect: speeding up would require a decrease in mass (not the case), same velocity would require mass to remain same (not the case), and there's no "slow for an instant then speed up" as momentum conservation with increased mass leads to lower speed.

Answer:

The objects will slow down after they collide.