A particle with electric charge $q$ moves along a straight line in a uniform electric field $\overrightarrow{\mathbf{E}}$ with speed $u$. The electric force exerted on the charge is $q \overrightarrow{\mathbf{E}}$. The velocity of the particle and the electric field are both in the $x$ direction. (a) Show that the acceleration of the particle in the $x$ direction is given by $$a=\frac{d u}{d t}=\frac{q E}{m}\left(1-\frac{u^{2}}{c^{2}}\right)^{3 / 2}$$ (b) Discuss the significance of the dependence of the acceleration on the speed. (c) What If? If the particle starts from rest at $x=0$ at $t=0,$ how would you proceed to find the speed of the particle and its position at time $t ?$