Velocity Ramp

A function f can be used to describe an object's position (say, on a track) based on time (t).

The derivative of the function f, written as f′, can be thought of (loosely) as the "slope" or "steepness" of the function f at any given time, that is, how quickly f is changing position around time t.

If f describes the position of an object, then f′ describes the velocity of the object.

In this game, a function f will follow your position based on time. The slope of the ramp at the end of the track will be set to the current value of f′.

What to grasp: The faster you are going, the steeper the slope is of the function tracking your position.

(Higher velocity = steeper slope.)

Velocity of an object can be negative, for instance if the object is moving backwards from the direction you are tracking.

However, the absolute value of the velocity is never negative. This value is the speed of the object, or how quickly its position is changing in any direction.

f′(t) = velocity of f′ with respect to t
|f′(t)| = speed of f′ with respect to t