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

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 object's momentum changes.

A large impulse is delivered to the object.

The object's momentum remains constant.

The impulse increases, leading to a greater change in momentum.

The impulse from the brakes changes the car's momentum, causing it to slow down.