Captain American throws his shield straight down off a roof with a speed of 50 m/s . What is the acceleration of the shield halfway down to the ground?

IF this is happening on Earth, then the acceleration of gravity wherever the captain and the roof are is about 9.8 m/s² downward.

IF his shield is not affected by air resistance, and it's free to behave under the influence of gravity alone, then its acceleration is 9.8 m/s² downward, from the moment it leaves his hand until the moment it hits a building, a tree, a car, a bus, an evildoer, or the ground.  

Whatever speed it has when it leaves his hand, in whatever direction, makes no difference.

conduction, convection, radiation

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)