1F = q(E + vXB)
break in component form to get
mx'' = qz'B............1
my'' = -qE.............2
mz'' = -qx'B............3
manipulate eqn 1 and 3 to get the eqn given in Q3
to solve the diff eqn make the subst : dx/dt = Y(some other variable)
u || get something like Y'' = (qB/m)^2Y
solve to get x= Asin qb/m(t -t(0) ) + c where t(0) and A and care constants
apply boundary conditions on dx/dt | any time t< (given) = v/2
and x = v/2*t' at t= t' (t' is given)
this way u get eqn of x(t)
from this u can get everything which has been asked
for Q2) if u || solve u || see x' = v/2 , y' = v/2 , z' = root3 v /2 so net speed is v at that instant
that time u can calculate using when y = 0 (that is easy , only acc(-) in y direction qE/m,simple kinematical eqn..put this time in the eqn of x and z(x' and z') to get the corresponding velocities (x' and z' )
