F⃗ = ma⃗

∫_{t_{1}}^{t_{2}} F⃗ dt = ∫_{t_{1}}^{t_{2}} ma⃗ dt

∫_{t_{1}}^{t_{2}} F⃗ dt = m∫_{t_{1}}^{t_{2}} a⃗ dt

∫_{t_{1}}^{t_{2}} F⃗ dt = m(v⃗_{2} − v⃗_{1})

∫_{t_{1}}^{t_{2}} F⃗ dt = (mv⃗_{2}) − (mv⃗_{1})

∫_{t_{1}}^{t_{2}} F⃗ dt = p⃗_{2} − p⃗_{1}

\frac{dp⃗}{dt} = ∑ F⃗_{ext}

\frac{dp⃗_{tot}}{dt} = 0 ⇒ p⃗_{tot} = constant

p⃗_{B} − p⃗_{A} = ∫_{A}^{B} F_{ext} dt

final p_{x} = initial p_{x}

final p_{y} = initial p_{y}

final p_{z} = initial p_{z}

p⃗_{final} = p⃗_{initial}

∫_{t_{1}}^{t_{2}} F⃗ dt = F⃗_{avg}∫_{t_{1}}^{t_{2}} dt = F⃗_{avg} (t_{2} − t_{1})