What potential difference is needed to stop an electron that has an initial velocity v=6.0

Formula for kinetic energy of an object:

KE = 0.5mv²

m is the mass and v is the velocity.

Formula for the work done on a charged object by moving it through a potential difference:

W = ΔVq

ΔV is the potential difference and q is the charge of the object.

To find the potential difference needed to decelerate an electron to rest, set the work done on the electron equal to its kinetic energy:

W = KE

Substitute W = ΔVq and KE = 0.5mv²

ΔVq = 0.5mv²

Given values:

q = 1.6*10⁻¹⁹C

m = 9.11*10⁻³¹kg

v = 6.0m/s

Plug in the given values and solve for ΔV

ΔV*1.6*10⁻¹⁹ = 0.5*9.11*10⁻³¹*6.0²

ΔV = 1.02*10⁻¹⁰V