A $4.00\text{ kg}$ cart initially at rest is acted on by a constant horizontal force of $800\text{ N}$ for $0.120\text{ s}$. Determine the impulse and final speed.

A stationary $2.00\text{ kg}$ block experiences the triangular force pulse shown. The force rises to $500\text{ N}$ at $0.020\text{ s}$ and returns to zero at $0.050\text{ s}$. Determine its speed after the pulse.

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A $0.145\text{ kg}$ baseball approaches a batter at $40.0\text{ m/s}$ and leaves in the opposite direction at $50.0\text{ m/s}$. Determine the magnitude of the impulse delivered by the bat.

For the baseball in the preceding problem, contact lasts $1.50\text{ ms}$. Determine the average force magnitude.

A $1500\text{ kg}$ car moving at $20.0\text{ m/s}$ rear-ends a stationary $1000\text{ kg}$ car. The vehicles lock together. Determine their common speed immediately after impact.

A $2.00\text{ kg}$ ball moving right at $5.00\text{ m/s}$ collides head-on with a $3.00\text{ kg}$ ball moving left at $2.00\text{ m/s}$. The coefficient of restitution is $e=0.80$. Determine both final velocities.

A $1.00\text{ kg}$ cart moving at $4.00\text{ m/s}$ strikes a stationary $3.00\text{ kg}$ cart in a one-dimensional perfectly elastic collision. Determine the final velocities.

A $1200\text{ kg}$ car travels east at $15.0\text{ m/s}$ and collides with a $1500\text{ kg}$ truck traveling north at $10.0\text{ m/s}$. They lock together. Determine the magnitude and direction of their common velocity.

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Two equal $1.00\text{ kg}$ disks collide on a frictionless plane. Before impact, disk A has velocity $(4.00\hat i+2.00\hat j)\text{ m/s}$ and disk B is at rest. The line of impact is the $x$-axis and $e=0.50$. Determine both final velocity vectors.

A $2.00\text{ kg}$ cart moves at $5.00\text{ m/s}$ and a $3.00\text{ kg}$ cart moves oppositely at $1.00\text{ m/s}$. Determine the center-of-mass velocity and both velocities in the COM frame.

An ideal rocket has effective exhaust speed $v_e=2500\text{ m/s}$, initial mass $m_i=12{,}000\text{ kg}$, and final mass $m_f=7000\text{ kg}$. Neglect external impulse during the burn. Determine the ideal velocity increment.