Notion of impulse

• An impulse \(J\) is the integrated force over time \(\displaystyle J=\int_{t_1}^{t_2} F(t)\,\mathrm{d}t\)
• • \(\rightarrow\) results in a sudden change of speed (/momentum) in a discrete case

• For a particle with constant mass
• • \(\displaystyle \int_{t_1}^{t_2} F(t)\,\mathrm{d}t = \int_{t_1}^{t_2} m\,a(t)\;\mathrm{d}t\)
  • \(\Rightarrow J = m\left(v(t_2)-v(t_1)\right)\)

• For an impact \(v\to v^{new}\)
• • \(v^{new}=v+J/m\)