Fluid Drag Proportional to Velocity
An object of mass m moves horizontally through a fluid with an initial velocity v₀. The object is subject to a resistive drag force from the fluid that is directly proportional to its velocity, F = -kv, where k is a positive constant. Which of the following expressions correctly describes the velocity v of the object as a function of time t?
A
v = v₀e^(-kt/m)
B
v = v₀ - kt/m
C
v = v₀(1 - e^(-kt/m))
D
v = v₀/(1 + kt/m)
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