A \(0.25\,\mathrm{kg}\) ball moves at \(16\,\mathrm{m\,s^{-1}}\). Find its momentum magnitude.

A constant \(12\,\mathrm{N}\) force acts for \(0.50\,\mathrm{s}\). Find the impulse magnitude.

A \(0.15\,\mathrm{kg}\) ball moves right at \(10\,\mathrm{m\,s^{-1}}\), then rebounds left at \(6.0\,\mathrm{m\,s^{-1}}\). Find the impulse on the ball, taking right as positive.

A \(0.060\,\mathrm{kg}\) ball moving at \(30\,\mathrm{m\,s^{-1}}\) is stopped in \(0.010\,\mathrm{s}\). Find the average force on the ball.

A force-time graph is triangular with height \(80\,\mathrm{N}\) and base \(0.20\,\mathrm{s}\). The impulse acts on a \(2.0\,\mathrm{kg}\) object initially at rest. Find its final speed.

A \(3.0\,\mathrm{kg}\) object initially at rest receives impulse \(\vec{J}=6\hat{\imath}-2\hat{\jmath}\,\mathrm{N\,s}\). Find its final velocity vector.

A force of \(30\,\mathrm{N}\) acts for \(0.20\,\mathrm{s}\), then \(10\,\mathrm{N}\) acts in the opposite direction for \(0.30\,\mathrm{s}\). Find the net impulse.

Two safety pads bring the same runner to rest. Pad A stops the runner in \(0.10\,\mathrm{s}\); pad B stops the runner in \(0.40\,\mathrm{s}\). Compare the average stopping forces and interpret the result.

A \(0.50\,\mathrm{kg}\) puck hits a wall and rebounds with half its incoming speed. The contact lasts \(0.020\,\mathrm{s}\), and the average force magnitude from the wall is \(90\,\mathrm{N}\). Find the incoming speed. State the sign convention and the modeling assumption.

A mass \(m\) moves in the positive \(x\)-direction with speed \(u\). During \(0<t<\tau\), a force pulse acts in the negative \(x\)-direction with magnitude \(F(t)=F_0(1-t/\tau)\). Derive the condition on \(F_0\tau\) for the mass to leave with speed at least \(\beta u\) in the negative \(x\)-direction. State assumptions.