Rod Travel

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Need help.. please with electric field.?

An insulating rod having linear charge density
57 μC/m and linear mass density 0.1 kg/m is
released from rest in a uniform electric field
135 V/m directed perpendicular to the rod.

Determine the speed of the rod after it has
traveled 3 m. Answer in units of m/s.
Please explain
thank u so much

Calculate the acceleration of a length L of the rod:

The force on the rod is F = q*L*E where q is the linear charge density; the mass of the rod is m = ρ*L where ρ is the linear mass density

a = F/m = q*L*E/ρ*L = q*E/ρ

The distance the rod travels in time t is s = 0.5*a*t²; the velocity at time t is v = a*t. t = v/a, so in terms of v, s = 0.5*v²/a. solve for v to get

v = √[2*a*s]

v = √[2*q*E*s/ρ]

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