1V
2kΩ
0.5µF
5mA
1kΩ

vc(0-) = -1 V ; ic(0+) = -1 mA
vc(∞) = 5 V ; ic(∞) = 0 mA
τ = 0.5 ms

vc(t) = 5 - 6e-2000t [V] ; t ≥ 0
time for vc to reach 0V: 0.091ms

ic(t) = -1 - 1e-2000t [V] ; t ≥ 0
time for ic to reach 0A: never, but 2.5ms is close