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.[br][br]Thanks to J Mulholland - this is his applet originally