Physics, 11.01.2021 21:00 GEEKLIFE6598

a proton travelling along is x-axis is lowed by a niform electric field E. at x = 20.0 cm, the proton has a speed of 3.5x10^6 m/s and at 80.0 cm the speed is zero. Determine the magnitude and direction of e,

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Answer from: citlalli30

Magnitude of electric field is 1.06 x 10^5 V/m along negative X-direction

Explanation:

Given: initial velocity of proton = u = 3.5 x 10^6 m/s

final velocity of proton = v = 0 m/s

initial point l_i = 0.2 m and final point is l_f = 0.8 m

According to conservation of energy:

change in in kinetic energy = change in potential energy of proton

⇒ $\frac{m}{2}(v^2-u^2 ) = qE(l_i - l_f)$

where q and m is the charge and mass of proton E is the electric field , l_i and l_f is the initial and final position of proton

on substituting the respected values we get,

1.023 x 10^-^1^4 = 9.6 x 10^-^2^0 x E

⇒ E = 1.06 x 10^5 V/m

external force is opposite to the motion as velocity of proton decreases with distance.

Therefore, magnitude of electric field is 1.06 x 10^5 V/m along negative X-direction

Answer from: Quest

i don't understand is there any other way you can rephrase it plz let me know in the comments and i will do it.

explanation:

Answer from: Quest

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

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

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

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a proton travelling along is x-axis is lowed by a niform electric field E. at x = 20.0 cm, the proto...