Higher-order derivatives are really important when we talk about how things move.

1. Acceleration:
   This is the second derivative of position, written as $\frac{d^2x}{dt^2}$.
   It tells us how velocity changes over time.
   For example, if something is moving faster and faster upwards, we say it has positive acceleration.
   This means its speed is increasing.

2. Jerk:
   This is the third derivative, written as $\frac{d^3x}{dt^3}$.
   Jerk helps us understand how acceleration changes.
   Think about a car that is speeding up.
   If the driver suddenly slams on the brakes, the jerk becomes negative.
   This shows that the car is slowing down quickly.

Knowing about these derivatives helps us understand different types of motion!