Determine the distance and time for each particle to acquire a kinetic energy of 3.2×10−16J. 3.2 × 10 −16 J .

Question

An electron and a proton, each starting from rest, are accelerated by the same uniform electric field of 200 N/C. Determine the distance and time for each particle to acquire a kinetic energy of 3.2×10−16J.3.2×10−16J.

Answer 1

qEd = 1/2mv² - 0J = 3.2E-16J

qE is the net force on each particle, since both have the same charge, the magnitude of the force is the same for both particles.

The product qEd (the net work) is the same for both and given in the problem (the directions of motion for each particle would be opposite the other).

Since the masses of the particles are different the speeds when they reached 3.2E-16J would be different.

You need only solve for d for each particle but since the kinetic energies are the same, the answers are the same.

Solving the individual velocities and using the simple constant acceleration equation for average velocity = displacement/Δt you can solve for time, For this case 2d/v = Δt.

I'll leave it to you to input 1) the charge and Electric fields to determine d and 2) the masses of the particles to find the speeds and ultimately the time to attain those speeds.