Question

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)

Answer 1

Correct option is D.
$$F = ma$$

$$qE = ma$$

$$a = \dfrac{qE}{m}$$

$$V \dfrac{dv}{dx} = \dfrac{qE}{m}$$

$$\displaystyle \int_0^V = Vdv = \int_0^x \dfrac{qE}{m}dx$$

$$\left[\dfrac{V^2}{2}\right]_0^V = \left[\dfrac{qE}{m}x\right]_0^x$$

$$\dfrac{V^2}{2} = \dfrac{qE}{m}x$$

$$V^2 = \dfrac{2qE}{m}x$$ equation of parabola