An electron is released from rest at a distance of 9.00 cm from a proton. If the proton is 11) held in place, how fast will the electron be moving when it is 3.00 cm from the proton?

Vf = 1.43 m/s

Explanation:

From Coulomb's Law, the electrostatic force between electron and proton is given as:

F = kq₁q₂/r²

F = Electrostatic force = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

q₁ = magnitude of charge on electron = 1.6 x 10⁻¹⁹ C

q₂ = magnitude of charge on proton = 1.6 x 10⁻¹⁹ C

r = distance between electron and proton = 9 cm = 0.09 m

Therefore,

F = (9 x 10⁹ N.m²/C²)(1.6 x 10⁻¹⁹ C)(1.6 x 10⁻¹⁹ C)/(0.09 m)²

F = 2.84 x 10⁻²⁶ N

but, from Newton's second law:

F = 2.84 x 10⁻²⁶ N = ma

where,

m = mass of electron = 9.1 x 10⁻³¹ kg

a = acceleration of electron = ?

Therefore,

2.84 x 10⁻²⁶ N = (1.67 x 10⁻²⁷ kg)(a)

a = 2.84 x 10⁻²⁶ N/1.67 x 10⁻²⁷ kg

a = 17.03 m/s²

Now, we apply 3rd equation of motion to the motion of electron from a distance of 9 cm to 3 cm near to the proton:

2as = Vf² - Vi²

where,

s = distance traveled = 9 cm - 3 cm = 6 cm = 0.06 m

Vf = speed of electron when it is 3 cm from proton = ?

Vi = Initial speed of electron = 0 m/s

Therefore,

2(17.03 m/s²)(0.06 m) = Vf² - (0 m/s)²

Vf = √2.04 m²/s²

Vf = 1.43 m/s

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles

b. a lightning bug, plug of grass, and a worm