In physics, impulse and momentum are two closely related concepts that help us understand the motion of objects. Impulse refers to the change in momentum that occurs when a force is applied to an object for a certain amount of time. It can be calculated using the formula:

where $J$ is the impulse, $F$ is the force applied, and $\Delta t$ represents the time interval over which the force acts. Impulse is a vector quantity, meaning it has both magnitude and direction.

Momentum, on the other hand, is a property of an object in motion and is defined as the product of its mass and velocity. It is given by the equation:

where $p$ is the momentum, $m$ is the mass of the object, and $v$ is its velocity.

The impulse-momentum theorem states that the impulse experienced by an object is equivalent to the change in its momentum. Mathematically, this can be expressed as:

This theorem is a powerful tool that allows us to analyze and solve various problems involving the motion of objects.