a proton accelerates from rest in a uniform electric field of 640 N/C At some time later its speed is 1.2x10^6

Question

A)find the magnitude of acceleration of the proton
B)how long does it take the proton to reach its speed
C)how far has it moved in that interval
D)What is the kinetic energy at the later time

Answer 1

Ok, here we have to remember the mass of the proton and the charge of the proton.

The charge of the proton is the same of the electron, but of course, it's positive :

q = 1.6*10^-19 C

mass proton = 1840*mass electron :

mass pronto = 1840*9.1*10^-31 kg

a) acceleration :

Using Newton's second Law :

F = m*a

Fe = electric force = E.q

E.q = m*a

640*1.6*10^-19 = 1840*9.1*10^-31*a

a = 0.06*10^12 = 6*10^10 m/s^2

b) Ok, to find the time, we use the acceleration, final speed and initial speed :

a = Vf - Vo / t

Vo = initial speed = 0 m/s

t = 1.2*10^6 / 6*10^10 = 0.2*10^-4 seconds.

c) To find, how far has it moved :

X = Vo*t + a*t^2 / 2

Vo = 0 m/s, then :

X = 6*10^10*(0.2*10^-4)^2 / 2

X = 0.24*10^2 / 2 = 12 meters

d) the kinetic energy at the later time when its speed is 1.2*10^6 m/s

KE = 1/2*1840*9.1*10^-31*(1.2*10^6)^2

KE = 1.2*10^-15 (Joules)

Hope that helped.

Note : Check the answers, but those are the steps ok.