Answer:
(a). The magnitude of the acceleration of the proton is ![5.74\times10^{13}\ m/s^2](https://tex.z-dn.net/?f=5.74%5Ctimes10%5E%7B13%7D%5C%20m%2Fs%5E2)
(b). The initial peed of the protion is ![2.83\times10^{6}\ m/s](https://tex.z-dn.net/?f=2.83%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(c). The time is
.
Explanation:
Given that,
Electric field ![E=-6.00\times10^{5}i\ N/C](https://tex.z-dn.net/?f=E%3D-6.00%5Ctimes10%5E%7B5%7Di%5C%20N%2FC)
Time = 5.0 sec
Distance 7.00 cm
(a). We need to calculate the acceleration
Using formula of force
![F=F_{e}](https://tex.z-dn.net/?f=F%3DF_%7Be%7D)
![ma=qE](https://tex.z-dn.net/?f=ma%3DqE)
![a=\dfrac{Eq}{m}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7BEq%7D%7Bm%7D)
Where, E = electric field
m = mass of proton
q = charge of proton
Put the value into the formula
![a=\dfrac{-6.00\times10^{5}\times1.6\times10^{-19}}{1.67\times10^{-27}}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B-6.00%5Ctimes10%5E%7B5%7D%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%7D%7B1.67%5Ctimes10%5E%7B-27%7D%7D)
![a=-5.74\times10^{13}\ m/s62](https://tex.z-dn.net/?f=a%3D-5.74%5Ctimes10%5E%7B13%7D%5C%20m%2Fs62)
The magnitude of the acceleration of the proton is ![5.74\times10^{13}\ m/s^2](https://tex.z-dn.net/?f=5.74%5Ctimes10%5E%7B13%7D%5C%20m%2Fs%5E2)
(b). We need to calculate the initial peed
Using equation of motion
![v^2-u^2=2as](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as)
Where, s = distance
Put the value into the formula
![0-u^2=2\times(-5.74\times10^{13})\times7.00\times10^{-2}](https://tex.z-dn.net/?f=0-u%5E2%3D2%5Ctimes%28-5.74%5Ctimes10%5E%7B13%7D%29%5Ctimes7.00%5Ctimes10%5E%7B-2%7D)
![u=\sqrt{2\times5.74\times10^{13}\times7.00\times10^{-2}}](https://tex.z-dn.net/?f=u%3D%5Csqrt%7B2%5Ctimes5.74%5Ctimes10%5E%7B13%7D%5Ctimes7.00%5Ctimes10%5E%7B-2%7D%7D)
![u=2834783.94](https://tex.z-dn.net/?f=u%3D2834783.94)
![u=2.83\times10^{6}\ m/s](https://tex.z-dn.net/?f=u%3D2.83%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
The initial peed of the protion is ![2.83\times10^{6}\ m/s](https://tex.z-dn.net/?f=2.83%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(c). We need to calculate the time interval over which the proton comes to rest
Using formula
![t=\dfrac{u}{a}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bu%7D%7Ba%7D)
Where, u = initial velocity
a = acceleration
Put the value into the formula
![t=\dfrac{2.83\times10^{6}}{5.74\times10^{13}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B2.83%5Ctimes10%5E%7B6%7D%7D%7B5.74%5Ctimes10%5E%7B13%7D%7D)
![t=0.493\times10^{-7}\ sec](https://tex.z-dn.net/?f=t%3D0.493%5Ctimes10%5E%7B-7%7D%5C%20sec)
Hence, (a). The magnitude of the acceleration of the proton is ![5.74\times10^{13}\ m/s^2](https://tex.z-dn.net/?f=5.74%5Ctimes10%5E%7B13%7D%5C%20m%2Fs%5E2)
(b). The initial peed of the protion is ![2.83\times10^{6}\ m/s](https://tex.z-dn.net/?f=2.83%5Ctimes10%5E%7B6%7D%5C%20m%2Fs)
(c). The time is
.