If a particle has negative acceleration then it must be slowing down, right?[br][br]Nope. Sorry. Try again. This is an extremely common misconception.[br][br]This applet is intended to address this misconception and help you understand what the sign of the first and second derivative is telling you.[br][br]The sign of the first derivative indicates the [b]direction of motion[/b], whereas the sign of the second derivative indicates the [b]direction of the acceleration[/b].[br][br]A particle is [b]slowing down[/b] if it is [b]accelerating in the opposite direction[/b] from which it is [b]moving[/b]. 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[br][br][math]s\left(t\right)=20sin\left(t\right)[/math].[br][br]If you wish to change the function, type a new one in the input field. For example, type s(t)=20*sin(t).