Originally posted by: Fenixgoon
Originally posted by: ledjani
Well I believe the answer is 0. The derivative of the velocity is acceleration. Thus whenever the graph of the velocity reaches its max, the derivative is 0. Thus the acceleration is 0. Because it is at rest acceleration wise, it has reached the top, and it isn't going up or down anymore.
WRONG. please retake physics/ calc
The question is somewhat unclear. It should say "assuming the particle has no other force acting on it" or something. It's kinda of unclear.
Assuming the only force is gravity though, the answer is 9.81m/s. It's not 0. Why? lenjani is right, derivative of velocity is acceleration, but velocity doesn't reach a so called "max", and that's where you make your mistake. Here's the connection you're missing. Derivative of position vs time gives you velocity. The position vs time graph is parabolic and upside down (think -x^2) thus it will have a max height.
The derivative of such a graph will intuitively be linear (think a straight line) with a negative slope and an x-intercept at the time where the position is a max. This is your velocity.
Finally, take the derivative of that velocity (a straight line), and you will get a constant. In the case of gravity being the only force at work, it's -9.81. Given that the question wants the value of the magnitude, you treat that acceleration as a vector, and take it's magnitude, which is always positive, and that is 9.81.