A proton accelerates from rest in a uniform electric field of 610 N/C. At some later time, its speed is 1.4 106 m/s.
(a) Find the magnitude of the acceleration of the proton.
m/s2

(b) How long does it take the proton to reach this speed?
µs

(c) How far has it moved in that interval?
m

(d) What is its kinetic energy at the later time?
J

Part(a): the acceleration of the proton is .

Part(b): the time taken by the proton to achieve the given velocity is .

Part(c): the distance travelled by the proton is .

Part(d): the kinetic energy of the proton is .

Explanation:

We know whenever a charge 'q' is placed in a uniform electric field, it will experience a force (F) of magnitude F = qE.

Part(a):

If 'a' be the acceleration gained by the proton when it is placed in the electric field 'E' and if '' be the mass of the proton, then

Given, and we know that the mass of proton . From equation(1)

Part(b):

If 'v' be the final velocity of the proton and 't' be the time required to this velocity, then, as the proton starts from rest,

Part(c):

If the proton travels a distance 'S' with acceleration a = in time t = , then the proton will move by a distance of S, given by

Part(d):

Kinetic energy (K) of a particle of mass 'm', moving with a velocity 'v' is given by

Here, .

So, the kinetic energy of the proton at later time is