Walking into a lamppost

Starting from rest, you begin walking, bringing your momentum up to 100 kg·m/s. You walk straight into a lamppost. Why is the momentum change of -100 kg·m/s caused by the lamppost so much more painful than the change of +100 kg·m/s when you started walking?

The situation is one-dimensional, so we can dispense with the vector notation. It probably takes you about 1 s to speed up initially, so the ground's force on you is F = Δp/Δt ≈ 100 N. Your impact with the lamppost, however, is over in the blink of an eye, say 1/10 s or less. Dividing by this much smaller Δt gives a much larger force, perhaps thousands of newtons. (The negative sign simply indicates that the force is in the opposite direction.)