# Step 03 — Integration (moving over time)

## Concept

"Integration" sounds like calculus, but the version we need is one line. An
object has a **position** and a **velocity**. Each frame we advance the position
by the velocity, scaled by how much time passed:

```
newPosition = position + velocity * delta
```

That's `add(pos, scale(vel, delta))`. This single step is the beating heart of
every game's update loop.

### Why `delta`?

`delta` is the number of **milliseconds since the last frame**. Frames are not
evenly spaced — a busy frame takes longer. If you moved a fixed amount *per
frame* instead of *per millisecond*, your game would run faster on a fast
computer and slower on a slow one.

By storing velocity as **units-per-millisecond** and multiplying by `delta`, the
distance travelled over a given stretch of real time is the same no matter how
the frames are chopped up. That property is called **framerate independence**,
and one of the tests below proves it: moving once with `delta = 16` lands in the
same place as moving sixteen times with `delta = 1`.

## Task

Implement `integrate(pos, vel, delta)` in `motion.ts`.

```sh
bun test workshop/steps/03-integration
```