The impulse is equal to the area under the force-time graph between the initial and final times.

The net external force is equal to the slope of the momentum-time graph at a given point in time.

1. Determine the initial momentum ($\vec{p}_0$). 2. Determine the final momentum ($\vec{p}$). 3. Subtract the initial momentum from the final momentum: $\Delta \vec{p}=\vec{p}-\vec{p}_{0}$

1. Identify the net force as a function of time, $\vec{F}_{\text {net }}(t)$. 2. Determine the time interval $[t_1, t_2]$. 3. Integrate the force function over the time interval: $\vec{J}=\int_{t_{1}}^{t_{2}} \vec{F}_{\text {net }}(t) d t$.

1. Identify the impulse acting on the object. 2. Identify the initial and final momentum of the object. 3. Set the impulse equal to the change in momentum: $\vec{J} = \Delta \vec{p}$. 4. Solve for the unknown quantity.

The momentum of the system changes at a rate proportional to the net external force: $\vec{F}_{\text {net }}=\frac{d \vec{p}}{d t}$

A large impulse results in a large change in the object's momentum.

A large area under the force-time graph indicates a large impulse delivered to the object.

Applying a constant net force over time results in a uniform change in momentum.

The object experiences a change in momentum and exerts an equal and opposite impulse on the wall.

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