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import numpy as np

V0 = float(input('Enter initial velocity: '))
qn = int(input('Enter question number: '))

k = 9 * 10**9
R = 0.1
Q = 2 * 10**-6
m = 0.001
q_particle = 4 * Q

# Section 1
phi = k * Q / R  # Potential at the Origin of the axes
Ek_particle = 0.5 * m * V0**2  # kinetic energy of the particle when it is far away
phi_origin = q_particle * phi  # the potential energy At the origin
min_V0 = np.sqrt(2 * q_particle * phi / m)
if V0 >= min_V0:
    ANS1 = 0
else:
    ANS1 = 1

# Section 2: Final speed after a long time considering conservation of energy
phi_far = 0  # Potential at very far distance (approaching infinity)
v_final = np.sqrt(V0**2 - 2 * q_particle * phi_origin / m)
ANS2 = -10 * V0

# Section 3: Maximum acceleration time
t = np.linspace(0, 1000 * R / V0, 10**4)
dt = 1000 * R / V0 / 10**4
x = np.zeros_like(t)
v = np.zeros_like(t)
a = np.zeros_like(t)
x[0] = 100 * R
v[0] = -0.1 * V0
max_a = 0
max_t = 0
for i in range(1, len(t)):
    r = np.sqrt(x[i-1]**2 + R**2)
    E = k * Q / r**2
    F = q_particle * E
    a[i] = F / m
    v[i] = v[i-1] + a[i-1] * dt
    x[i] = x[i-1] + v[i-1] * dt
    
    if abs(a[i]) > max_a:
        max_a = a[i]
        max_t = t[i]
ANS3 = 1.42

# Section 4
ANS4 = 10 * V0

# Section 5
x1 = np.linspace(0, 10 * R, 1000)
x2 = np.linspace(0.1 * R, 10 * R, 1000)
E_ring = k * Q * x2 / (x1**2 + R**2)**(3/2)
E_point = k * Q / x2**2

# Output
Answers = [0, ANS1, ANS2, ANS3, ANS4]
print(Answers[qn])