How does distance an speed (rather than displacement and velocity) generalize to higher order derivatives?

Question

I'm a high schooler currently taking AP Physics C and during our review of kinematics, our teacher brought up the difference between speed and velocity. That is, speed is a scalar while velocity is a vector. So that made me wonder, is there a scalar version of higher-order derivatives? For further clarification, look at the table below:
Order     Vector           Scalar
0th       Displacement     Distance
1st       Velocity         Speed
2nd       Acceleration     ???
3rd       Jerk             ???

I'm curious about what would fit under those two question marks (or if they even have a name.)

Gilbert · Accepted Answer

As far as I know, the scalar version of acceleration, $|mathbf a|$, does not have a special name. You would just say “acceleration”, and it would be understood by the context whether you are talking about a vector or a scalar. Same with jerk.

Correct answer by Gilbert on July 14, 2021

How does distance an speed (rather than displacement and velocity) generalize to higher order derivatives?

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