There is a question on p. 31 of our text, #21. It says that there is a particle moving along the x axis. It asks you to sketch a graph that is a possible description of position as a function of time for the following situations:
a) velocity is zero and acceleration is negative
b) velocity is zero and acceleration is positive
Can you describe situations where these conditions would occur?
Remember that velocity is the first derivative of position, and acceleration is the second derivative. So, you want to make a graph of x(t) which has a local maximum (for part a) and alternatively a local minimum (for part b).
An example of a physical situation for part (a) would be the moment when a ball that you have tossed upward reaches its maximum height. At that moment, the velocity if zero but the acceleration is still negative (-9.8m/s2). An example of a physical situation for part (b) would be the moment of impact when you bounce a hard ball (like a billiard ball) off of the floor. At that moment the velocity is zero, but the net acceleration is positive.