explain the method  to solve the below given question . do not only state the answer :

a particle moving in a straight line with uniform accleration is observed to be at distance 'a' from a fixed point initially. it is at distances b,c,d from the same point after n , 2n , 3n second. the acceleration of the particle is :

(a) c-2b+a / n to the power 2      (b) c+b+a / 9 x n to th power 2

(c) c+2b+a / 4 x n to the power 2      (d) c-b+a / n to the power 2

hi,refer to the figure for clarity

for the first n seconds.

let acceleration be w and initial velocity be u

 

b-a = un + 1/2wn²

 

For the first 2n seconds

 

c-a = 2un + 2wn²

 

 

2 equations 2 unknowns (u and w)

solve and you will get

w=(c + a - 2b) / n²