How do you find the magnitude of the average velocity?

Question

Jillian angrily throws her engagement ring straight up from the roof of a building, a height h above the ground with an initial speed of v, For the motion from her hand to the ground, what is the magnitude of the average velocity of the ring? What is the direction of the average velocity of the ring? For the motion from her hand to the ground, what is the magnitude of the average acceleration of the ring? What is the direction of the average acceleration of the ring? In how many seconds after being thrown does the ring strike the ground? What is the speed of the ring just before it strikes the ground?

Answer 1

This is a standard HS problem. Here are a few tips.
Taking up to be positive, the position of the ring as a function of time is
x(t) = h + v(t=0)t - gt^2/2
the velocity is
v(t) = v(t=0) - gt
the acceleration is
a(t) = -g
The average values are obtained by evaluating the above at time t and dividing by the elapsed time. To find the time to hit the ground, solve the first equation for x=0.