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Question
q)An electron of mass Me,initially at rest,moves through a certain distance in a uniform electric field in time t1. A proton of mass Mp also initially at rest,takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t2/t1 is nearly equal to/
a)1
b)Under root Mp/Me
c)Under root Me/Mp
d)1836

Answer
Hello Ishaan,

Since electrons and protons have charges of equal magnitude, forces of equal magnitude will be exerted on them. The direction of the force will be opposite of course. Newton's 2nd Law gives us the relationship between the force on these charges, their masses, and the acceleration they experience. The electron's acceleration is
a1 = F/Me
The proton's acceleration is
a2 = F/Mp

Use the kinematic formula
d = Vi*t + (1/2)*a*t^2
where Vi = 0 for both charges.
For the electron d = d1, a = a1, and t = t1
while for the proton d = d2, a = a2, and t = t2.

The problem says that d1 = d2 so
(1/2)*a1*t1^2 = (1/2)*a2*t2^2
(1/2)*(F/Me)*t1^2 = (1/2)*(F/Mp)*t2^2
The next step is to simplify and solve for t2/t1.

I hope this helps,
Steve

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Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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