A body of mass 2 slugs is dropped with initial velocity zero, but encounters air resistance that is equal to 4 times the square of its velocity

initial-velocity
square-of-velocity

#1

A body of mass 2 slugs is dropped with initial velocity zero, but encounters air resistance that is equal to 4 times the square of its velocity. Find an expression for the velocity of the body at time t in seconds.

Answer:

Initial velocity u = 0
Let velocity at any time t is v
Retardation r= 4v^2
Applying Law of Motion
V = u – rt
V = 0 – 4v^2t
4v^2t +v =0 , it is the desired expression of velocity in terms of time t