A particle moves in x-y plane with constant accelaration a directed along negative y- axis. the equation of motion of the particle has the form y=cx - bx^2, where c and b are constants. find the velocity of the particles at the origin of  cordinates.

the method is there and look at the comment

http://www.goiit.com/posts/list/community-shelf-a-problem-of-irodov-component-method-39256.htm

The given equation is analogous to that of a projectile fired from the ground. Compare the given equation with  

y = cx - bx²

differating it

u get v_y  = (c-2bx)v_x-------1

again differatating u get

a = 2bv_x ^2------------2

solve 1,2 fr v_x , v_y  

so with da values of v_x , v_y

_{u can find velocity at any point}    

My last reply was distorted. Here goes :

we have  and

Now you can solve for u.