Linear Momentum

A system of particles is moving with a constant center-of-mass velocity. Which of the following statements must be true?

Two particles with masses $m_1 = 2 kg$ and $m_2 = 3 kg$ are moving along the x-axis. Particle 1 has a velocity of $v_1 = 5 m/s$ and particle 2 has a velocity of $v_2 = -2 m/s$. What is the velocity of the center of mass of the system?

A 5 kg block is moving at 3 m/s on a frictionless surface when it collides head-on with a 2 kg block at rest. If the two blocks stick together after the collision, what is their final velocity?

A 2 kg ball moving at 5 m/s collides head-on with a 3 kg ball moving at -2 m/s. After the collision, the 2 kg ball moves at -1 m/s. What is the final velocity of the 3 kg ball?

A 1 kg ball moving at 10 m/s collides head-on with two stationary balls, each of mass 0.5 kg. After the collision, all three balls move separately along the same line. If the 1 kg ball stops completely, and one of the 0.5 kg balls moves at 4 m/s, what is the velocity of the other 0.5 kg ball?

A 2 kg object moving at 3 m/s in the positive x-direction collides with a 1 kg object moving at 4 m/s in the positive y-direction. If the two objects stick together after the collision, what is the magnitude of their final velocity?

A 1 kg ball moving at 5 m/s in the positive x-direction collides with a 1 kg ball at rest. After the collision, the first ball moves at 2 m/s at an angle of 30 degrees above the x-axis. What is the approximate speed of the second ball after the collision?

A 0.5 kg ball strikes a wall with a velocity of 10 m/s and bounces back with a velocity of -8 m/s. What is the magnitude of the impulse on the ball?

A 2 kg object's velocity changes from 5 m/s to 15 m/s in 4 seconds due to a constant force. What is the average force exerted on the object?

A 1 kg ball is dropped from a height and takes 3 seconds to reach the ground. Assuming negligible air resistance, what is the impulse on the ball due to gravity during this time?