A) what voltage will accelerate electrons to a speed of 6.00×10−7m/s? (b) find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-t field and compare this with the radius of curvature of an electron accelerated through the same potential.

a) V= 1.024×10∧-24V

b) Radius of curvature for electron =6.825×10∧-18 m

c) For proton r = 2.92×10∧-16 m

Explanation:

1. The total energy for the electric force is conserved

k1+u1=k2+u2

k1=u2=0

∴ k2=u1

∴ u1=㏑V, k∨2=1/2 mv²

Rearranging

V=mv²/2e =(9.1×10∧-31)×(6×10∧-7)²/2(1.6×10∧-19) = 1.024×10∧-24V

2. The radius of curvature for an electron accelerated in that potential is given by r=mv/qB =(9.1×10∧-31)×(6×10∧-7)/(1.6×10∧-19) (0.5) = 6.825×10∧-18 m

3. For a proton accelerated in the same potential

ev=1/2mv² =√2(1.6×10∧-19)( 1.024×10∧-24V)/1.67×10∧-27 = 1.401×10∧-8 ms-1

The radius of curvature for the proton is  r=mv/qB

1.67×10∧-27×1.401×10∧-8 ms-1/1.6×10∧-19×0.5 = 2.92×10∧-16 m

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russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.