If a particle has negative acceleration then it must be slowing down, right?
Nope. Sorry. Try again. This is an extremely common misconception.
This applet is intended to address this misconception and help you understand what the sign of the first and second derivative is telling you.
The sign of the first derivative indicates the direction of motion, whereas the sign of the second derivative indicates the direction of the acceleration.
A particle is slowing down if it is accelerating in the opposite direction from which it is moving. This means we also have to know its direction of motion to conclude anything about whether it is speeding up or slowing down.

The current position function is
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If you wish to change the function, type a new one in the input field. For example, type s(t)=20*sin(t).