I have some doubts on these problems Two particles, each having a mass of 3.0 mg

Question

I have some doubts on these problems
Two particles, each having a mass of 3.0 mg and an equal and opposite charge of 5.0 nC, are initially stopped at a distance of 5.0 cm and are freed at the same time. What is the velocity of both particles at the instant they are separated by 2.0 cm?

Two point-shaped charges of 8.0 C are placed on the x-axis at points x = ± 1.0 m and are freed at the same time. What is the kinetic energy of each particle, when it has traveled 2.0 m?
I have some doubts on these problems
Two particles, each having a mass of 3.0 mg and an equal and opposite charge of 5.0 nC, are initially stopped at a distance of 5.0 cm and are freed at the same time. What is the velocity of both particles at the instant they are separated by 2.0 cm?

Two point-shaped charges of 8.0 C are placed on the x-axis at points x = ± 1.0 m and are freed at the same time. What is the kinetic energy of each particle, when it has traveled 2.0 m?

Two particles, each having a mass of 3.0 mg and an equal and opposite charge of 5.0 nC, are initially stopped at a distance of 5.0 cm and are freed at the same time. What is the velocity of both particles at the instant they are separated by 2.0 cm?

Two point-shaped charges of 8.0 C are placed on the x-axis at points x = ± 1.0 m and are freed at the same time. What is the kinetic energy of each particle, when it has traveled 2.0 m?
Two particles, each having a mass of 3.0 mg and an equal and opposite charge of 5.0 nC, are initially stopped at a distance of 5.0 cm and are freed at the same time. What is the velocity of both particles at the instant they are separated by 2.0 cm?

Two point-shaped charges of 8.0 C are placed on the x-axis at points x = ± 1.0 m and are freed at the same time. What is the kinetic energy of each particle, when it has traveled 2.0 m?

Explanation / Answer

Question 1 :

m = mass of each particle = 3 x 10-3 kg

q = magnitude of charge on each particle = 5 x 10-9 C

ri = initial distance between the particles = 5 cm = 0.05 m

rf = final distance between the particles = 2 cm = 0.02 m

v = speed of each particle when they are at distance of 2 cm

using conservation of energy

Initial electric potential energy = kinetic energy + Final electric potential energy

Ui = KE + Uf

- k q2/ri = 2 (0.5) m v2 - k q2/rf

- (9 x 109) (5 x 10-9)2/(0.05) = 2 (0.5) (3 x 10-3) v2  - (9 x 109) (5 x 10-9)2/(0.02)

v = 0.061 m/s

Question 2 :

r = distance between the charges = 2 m

q = charge on each particle = 8 x 10-6 C

KE = ?

using conservation of energy

Kinetic energy gained = - electric potential energy lost

KE = k q2/r = (9 x 109) (8 x 10-6)2/(2)

KE = 0.288 J

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