Elastic Collisions — Prelims Questions

A body of mass $m_1$ moving with velocity $u_1$ undergoes a one-dimensional elastic collision with another body of mass $m_2$ at rest. If $m_1 = m_2$, what are the final velocities of the two bodies?

A $2\,\text{kg}$ mass moving at $10\,\text{m/s}$ undergoes a head-on elastic collision with a $3\,\text{kg}$ mass moving at $5\,\text{m/s}$ in the opposite direction. What is the relative speed of separation after the collision?

A ball of mass $m$ moving with velocity $v$ collides elastically with a stationary wall. What is the change in momentum of the ball?

In a one-dimensional elastic collision, which of the following statements is always true?

A $1\,\text{kg}$ ball moving at $4\,\text{m/s}$ collides elastically with a $3\,\text{kg}$ ball initially at rest. What is the final velocity of the $1\,\text{kg}$ ball?

Two particles of masses $m$ and $2m$ are moving with speeds $2v$ and $v$ respectively, in opposite directions. They undergo a one-dimensional elastic collision. If the initial kinetic energy of the system is $E$, what is the total kinetic energy after the collision?