The effect of a force acting over a time interval; a 'push' that changes momentum. Mathematically, it's the integral of force with respect to time: $\vec{J}=\int_{t_{1}}^{t_{2}} \vec{F}_{\text {net }}(t) d t$

Momentum is a measure of mass in motion; it is a vector quantity defined as the product of an object's mass and its velocity: $\vec{p} = m\vec{v}$

The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum: $\vec{J} = \Delta \vec{p}$

The vector sum of all forces acting on a system from outside the system. It dictates how quickly the momentum of the system changes.

The difference between the final momentum and the initial momentum of an object: $\Delta \vec{p}=\vec{p}-\vec{p}_{0}$

Impulse: The change in momentum of an object ($\vec{J} = \Delta \vec{p}$), caused by a force acting over time. | Momentum: The product of an object's mass and velocity ($\vec{p} = m\vec{v}$), representing its inertia in motion.

Force-time graph: Area under the curve represents the impulse. | Momentum-time graph: Slope of the curve represents the net force.

Constant mass: $\vec{F}_{\text {net }} = m\vec{a}$ applies, where mass is constant. | Variable mass: $\vec{F}_{\mathrm{net}}=\frac{d \vec{p}}{d t}=\frac{d m}{d t} \vec{v}$ applies, considering the rate of mass change.

Impulse (J) is the average force (F_avg) applied over a specific time interval (Δt): J = F_avg * Δt

Momentum (p) is the product of an object's mass (m) and its velocity (v): p = mv

Change in Momentum (Δp) is the difference between the final momentum (p) and the initial momentum (p₀): Δp = p - p₀

Net External Force (F_net) is the vector sum of all forces acting on an object or system.

The Impulse-Momentum Theorem states that the impulse acting on an object is equal to the change in momentum of that object: J = Δp