Kind of hard physics question? help please?

Start by finding the force on the electron:

F = Eq, where q is the electron charge:

F = (12.00 × 10⁴ N/C)(1.602 × 10ˉ¹⁹ C) = 1.922 × 10ˉ¹⁴ N.

F = ma, so a = F/m, where m is the electron mass:

a = (1.922 × 10ˉ¹⁴ N) / (9.109 × 10ˉ³¹ kg) = 2.110 × 10¹⁶ m/s².

x = x₀ + v₀t + ½at².

Here, x = the length of the journey from the centerline to one plate = 0.0100 m;

x₀ = 0 m;

v₀ = unknown, but it is the speed needed to travel the length of the plates (0.0600 m) in the time required to accelerate to one of the plates;

a = 2.110 × 10¹⁶ m/s².

In general, x = vt, so t = x/v, so we can get t = (0.0600 m) / v₀.

Rewrite the displacement equation above:

½at² + v₀t + x₀ = x.

Substitute (0.0600 m / v₀) for t, and put in the other values:

½(2.110 × 10¹⁶ m/s²)(0.0600 m / v₀)² + v₀(0.0600 m / v₀) + 0 m = 0.0100 m.

Simplify this to

½(2.110 × 10¹⁶ m/s²)(0.0600 m / v₀)² + 0.0600 m = 0.0100 m,

and then to

½(2.110 × 10¹⁶ m/s²)(0.0600 m / v₀)² = -0.0500 m.

Multiply by 2 for a bit more simplicity, giving

(2.110 × 10¹⁶ m/s²)(0.0600 m / v₀)² = -0.100 m.

Rewrite this as

(2.110 × 10¹⁶ m/s²)(0.00360 m² / v₀²) = -0.100 m.

Solving for v₀² gives

v₀² = (2.110 × 10¹⁶ m/s²)(0.0036 m²) / (-0.100 m)

= -7.596 × 10¹⁴ m²/s².

(I think we can safely assign a positive sign here; the choice of coordinate directions doesn't matter much. So. v₀² = +7.596 × 10¹⁴ m²/s².)

Now we can use this in the kinetic-energy equation.

K = ½mv₀²

= ½(9.109 × 10ˉ³¹ kg)(7.596 × 10¹⁴ m²/s²)

= 3.459 × 10ˉ¹⁶ J.

thanks for the long explanation, and for your time :)