In quadratic drag problem, the deceleration is proportional to the square of velocity

Part A

Given that 

Then, 



For , then



Thus, 

For , we have



Part B

Recall that from part A, 



Now, at initial position, t = 0 and , thus we have



and when the velocity drops to half its value,  and 

Thus,



Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by

The answer of the above is