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A particle of mass $$m$$ and charge $$q$$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $$v$$ on the distance $$x$$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)
For force acting on the particle: $$F = qE$$
For constant acceleration: $$a = \frac{qE}{m}$$
$$v^2 = u^2 + 2ax$$
$$v^2 = 2\left(\frac{qE}{m}\right)x$$
$$v = \sqrt{\frac{2qE}{m}} \cdot \sqrt{x}$$
This describes a sideways parabola ($$y^2 = 4ax$$) passing through the origin, where the slope decreases as $$x$$ increases.
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