Question

A particle with a specific charge s starts from rest in a region where the electric field has a constant direction, but whose magnitude increases linearly with time. The particle acquires a velocity v in time t. 

(a) v ∝ s 

(b) v ∝ √s 

(c) v ∝ t 

(d) v ∝ t²

Answer 1

Correct Answer is: (a) v ∝ s, (d) v ∝ t²

E = αt (α = constant) F = QE

a = F/m = QE/m = Es = αst.

∴ a = dv/dt = αst.

or v = 1/2 αst² 

∴ v ∝ s and t².

v = dx/dt = 1/2 αst²

or x = 1/6 αst³

or x ∝ t³.