When a charged particle having charge #q# is situated in an electric field #vecE#, the force #vecF=qcdotvecE#

Considering only the modulus part #|vecF|=qcdot|vec E|#

We also know from Newton's second law that Force #vecF=mcdot veca#, where #veca# is the acceleration.

again considering the modulus part

#|vecF|=mcdot |veca|#

Equating both we get

#mcdot |veca|=qcdot|vec E|#

or #|veca|=q/mcdot|vec E|#

Kinematic equation for a particle moving with constant acceleration is

#v^2-u^2=2as#,

where #v# is the final velocity, #u# is the initial velocity and #s# is the distance traveled. Inserting given values and solving for #v#

#v^2-0^2=2q/mcdot|vec E|s#

or #v^2=2 xx (3.2xx10^-19)/(6.4xx10^-27)cdot(1.6xx10^5)xx(2xx10^-2)#

or #v=sqrt( 3.2xx10^11)#

or #v=5.7xx10^5ms^-1#, rounded to first decimal place.