Google "jerk equations," select "images," and take some time with some of these graphs.

distance velocity acceleration

Notice that one line steps up and down in a pedal shape, like an accelerator or brake pedal?Another line slants? Another bends?

bend slant step

Make copies and make notes on them. Make notes just for yourself:

distance velocity acceleration

A step in the acceleration line slants the velocity line which bends the distance line.

The slant is the derivative of the bend, its rate of change. The step is the derivative of the slant.

In the other direction one line is the integral of another. The bend accumulates the slant: the distance is the integral of the velocity, the accumulation of the velocities. The slant accumulates the step(s): the velocity is the integral of the acceleration, the accumulation of the accelerations.

Get a feel for this.

Relate the graph to something happening all around you, some physics example:

ball on slope

Notice the difference between speed and velocity here. Any direction counts as speed. Speed in the wrong direction is lost velocity.

Find a graph with four lines, where the fourth is jerk. That's the jerk you feel when you put the pedal down in a Tesla and for an instant it mashes you into your seat and pulls your cheeks away from your teeth:


In notes to myself I shorten derivative to "derv." You OK with that?

Velocity is the derv of distance, acceleration the derv of velocity, jerk the derv of acceleration.

This makes acceleration the second derv of distance, jerk the third derv of distance, and me the derv jerk.

Find a graph that puts the four lines on top of one another:

lines superimposed

Make notes in color.

Note slopes.

Note the shape of the lines: the step of the jerk, the slant of acceleration, the bend of velocity, the slower bend of distance, lagging behind.

The integral smooths the line of the derv and lags it. The accumulation always lags the change it accumulates. The velocity smooths the slant of the acceleration after a lag. The distance smooths the slant of the velocity after a lag.

Get a feel for this. Get good at guessing one line from another.

Yes, you will see this on a test.