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.

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: $\Delta \vec{p}=\vec{p}-\vec{p}_{0}$

1. Determine the final momentum (p). 2. Determine the initial momentum (p₀). 3. Subtract the initial momentum from the final momentum: Δp = p - p₀.

1. Determine the average force (F_avg) acting on the object. 2. Determine the time interval (Δt) over which the force acts. 3. Multiply the average force by the time interval: J = F_avg * Δt.

1. Find the slope of the momentum-time graph at the desired point. 2. The slope represents the net external force at that instant: F_net = Δp/Δt.

1. Plot Force vs time on a graph. 2. Calculate the area under the force-time graph. 3. The area represents the total impulse delivered.

1. Start with the Impulse-Momentum Theorem: J = Δp. 2. Substitute J with F_net * Δt and Δp with m * Δv. 3. Rearrange the equation to get: F_net = m * (Δv/Δt) = ma.