voltage physics

Question

A proton is travelling at a speed of 4 x 105 m/s moves into a series of charged parallel plates as shown below.
a) What is the impact speed on the third plate?

(Plate 1 is 0V, plate 2 -1000V, plate 3 is -1500V)


b) Why can you not use high-school kinematics to get the answer above for this situation?

Answer 1

   I am assuming that there are holes in the intermediate plates to allow the proton to go from region to region until it impacts the last plate.

 

a) Use energy conservation.  

 

b) You actually can but there is a different acceleration for each region between the plates.

Answer 2

Here Gain in kinetic energy = Charge on Proton x Total Potential difference
= 1.6x 10^-19x (1500-0)   J
total energy 0f proton at the third plate = initial KE + gain in KE
= ½ mv² + 1.6 x 10^-19 x 1500
Where v=4x10⁵ m/s
Equating it to the final KE =½ mv_f ² = ½ mv² + 1.6 x 10^-19 x 1500 wher v_f is final speed of proton
Substituting m = 1.6x 10^-27 kg as mass of proton and v= 4x10⁵ we can calculate the value of vf , the velocity of proton striking the third plate