Two large aluminum plates are separated by a distance of 2.0 cm and are held at a potential difference of 170 V. An electron enters the region between them at a speed of 2.9 x 10^5 m/s by passing through a small hole in the negative plate and continues moving toward the positive plate. Assume the electric field between the plates is uniform.
(a) what is the electron's speed, in meters per second, when it is 0.1 cm from the negative plate?

Explanation:

Electric field between plates

V / d

= 170 / ( 2 x 10⁻² )

= 8500 N/C

Force on electron in this field

= 8500 x 1.6 x 10⁻¹⁹

= 13600 x 10⁻¹⁹ N

Acceleration

= 13600 x 10⁻¹⁹ / 9.1 x 10⁻³¹

a = 1494.5 x 10¹² m /s²

s = .1 x 10⁻² m

v² = u² + 2as

=  (2.9x 10⁵)²+ 2 x 1494.5 x 10¹² x .1 x 10⁻²

= 8.41 x 10¹⁰ + 299 x 10¹⁰

= (8.41 + 299 ) x 10¹⁰

v = 17.53  x 10⁵ m /s

the answer is b ) square root of 5

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s