Electric Forces and Fields, High School Physics?

1)
The force on a charge is:

F = q*E

In this case, the "q" is the electron charge, but positive: q = 1.6*10^-19 C.

F = 1.6*10^-19 * 25 = 4*10^-18 N

F = m*a

a = F/m

According to the listed reference, the mass of a proton is 1.672*10^-27 kg

a = 2*10^-18 / 1.672*10^-27 = 2.4*10^9 m/s^2

The acceleration is directed away from the sphere, since both charges are positive, and would therefore repel each other.

2)
Energy can be expressed in terms of electron volts.  This is one electron accelerated through 500V, or 500eV.  According to Google, 500 electron volts = 8.01 × 10-17 joules.  This is kinetic energy.  The mass of an electron is: 9.11*10^-31 kg.

KE = (1/2)*m*v^2

v = sqrt( 2*KE/m ) = sqrt( 2(8.01*10^-17) / 9.11*10^-31 ) = 13.3*10^6 m/s

3)

The electric field between the two plates is:

E = V/d = 8000 / .005 = 1.6*10^6 V/m

F = q*E = 1.6*10^-19 * 1.6*10^6 = 256*10^-15 N

a = F/m = 256*10^-15 / 1.672*10^-27 = 153*10^12 m/s^2 = 1.53*10^14 m/s^2  (is that a typo in the answer key?)

Presumably, it acquires 8000 eV of energy, or 1.28*10^-15 J, again kinetic energy.

v = sqrt( 2*KE/m ) = sqrt( 2*1.28*10^-15 / 1.672*10^-27 ) = 1.24*10^6 m/s