A proton and an $\alpha -$particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is

$$\begin{gathered} F= ma \\ \Rightarrow qE=ma \\ \Rightarrow a=\frac{qE}{m} \\ Now, y = \frac{1}{2}a{t}^2 \\ \Rightarrow y=\frac{Eq{t}^2}{2m} \\ \Rightarrow t^2 \propto \frac{m}{q} \\ {\left(\frac{t_p}{t_{\alpha }}\right)}^2=\frac{m_p}{m_{\alpha }}\times \frac{q_{\alpha }}{q_p} \\ =\frac{t_p}{t_{\alpha }}=\sqrt{\frac{1}{4}\times \frac{2}{1}}=\sqrt{\frac{1}{2}} \\ t_p:t_{\alpha }=1:\sqrt{2} \end{gathered}$$