Answer:
a) a = -g = 9.8 m/s²
, b) a = 0 m/s² and c) t1 = 0.0213 s
Explanation:
a) At the moment the marble is released its velocity is zero, so it has no resistance force, the only force acting is its weight, so the acceleration is the acceleration of gravity
a = -g = 9.8 m / s²
b) When the marble goes its terminal velocity all forces have been equalized, therefore, the sum of them is zero and consequently if acceleration is also zero
a = 0 m / s²
c) We have to assume a specific type of resistive force, for liquid in general the resistive force is proportional to the speed of the body.
The expression of this situation is
v = mg / b (1 - )
For a very long time the exponential is zero, so the terminal velocity is
= mg / b
b = mg /
b = 5 10-3 9.8 / 0.3
b = 0.163
We already have all the data to calculate the time for v = ½
½ = (1 -)
½ = 1- e (- 0.163 t1 / 5 10-3)
e (-32.6 t1) = 1-0.5 (by ln())
-32.6 t1 = ln 0.5
t1 = -1 / 32.6 (-0.693)
t1 = 0.0213 s