Impulse (physics)

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.