$7.1.3$ A particle with a charge $q$ and a mass $m$ passes through a region of a uniform electric field of length $d$ in time $t$. The velocity $v$ of a particle entering the field is directed along the field. Determine the electric field intensity.
The motion of particle is accelerated by electric field, so $$d = vt-\frac{at^2}{2} \;(1)$$ Applying Newton Second Law $$F = qE = ma$$ then, $$a = \frac{qE}{m} \;(2)$$ Putting $(2)$ into $(1)$ $$\boxed{E = 2m\frac{d-vt}{qt^2}}$$
BSc. Luis Daniel Fernández Quintana
Physics Department (FCNE)
Universidad de Oriente, Cuba