Impulse is force applied times amount of time it is applied for.

\[I = \vec{F}t\]

In other words, impule is a “compound” quantity, it has two parts 1) the force applied and 2) how long it is applied for.

When you apply a force on some object, you give it an acceleration. The longer you apply the force, the longer the object keeps on accelerating for, the more its velocity changes. Thus applying a force for a certain amount of time, results in a change in velocity for the object (the mass).

\[I = \vec{F}t = \Delta vm\]

Looking from another perspective, the amount of velocity change that an impulse causes on an object depends on the mass of the object.

\[\frac{I}{m} = \Delta v\]

Thus, when you apply an impulse (a force for some time) on an object (mass), the object’s velocity changes by some amount; the change in velocity is proportional (linear) to the quantity \(\frac{I}{m}\)

\[\Delta v \propto \frac{I}{m}\]

In other words, the change in velocity is directly proportional to \(I\) and inversely proportional to \(m\)

\[\Delta v \propto I\] \[\Delta v \propto \frac{1}{m}\]

Let’s make it concrete. Let’s say we have a 1 kg object at rest. We apply an impulse of 100 to it. How much would the velocity change by?

\[\Delta v = \frac{I}{m} = \frac{100}{1} = 100\ m/s\]

Since the object started at speed 0, it will be up to 100 m/s now.

What if the object was 2 kg instead of 1? Well, then the speed would only change by 50 m/s. The heavier the object, the less this impulse will change its velocity.