Physics

The impulse–momentum theorem is the key: force integrated over time ($\int F \, dt$) equals the total impulse delivered to a particle, which by Newton's second law ($F = \frac{dp}{dt}$) must equal the change in momentum ($\Delta p$). Graphically, the area under an $F$–$t$ curve represents exactly this integral, so it directly measures how much momentum the particle gains or loses.

The impulse–momentum theorem is the key: force integrated over time ($\int F \, dt$) equals the total impulse delivered to a particle, which by Newton's second law ($F = \frac{dp}{dt}$) must equal the change in momentum ($\Delta p$). Graphically, the area under an $F$–$t$ curve represents exactly this integral, so it directly measures how much momentum the particle gains or loses.