A particle is moving in a straight line with constant acceleration. If x,y and z be the distances described by a particle during the pth, qth and rth second respectively, prove that

Explanation

Let (u) be the initail velocity of the particle and (A) b its uniform acceleration . Using the
relation, ` D_(n) =u + a/2 (2n -1), we have
`a =u + A/2 (2 l -1 ) ` ….(i)
`b=u + A/2 (2m -1)` …(ii)
` and `c= u + A/2 ( 2n -1) ` ..(iii)
`Subtracting (iii) from (ii),,
` b-c = A/2 (2 m-2n) = A (m-n)`
or ` a (m -n) =a 9b-c)//A`
`=(ab-ac)//A ...(v)
` Subtracting (ii) from (i),
` a-b =A/2 (2l -2m) =A (l-m)`
or ` c( l-m) = c (a -b)//A = (ac-bc) //A` ......(vi)
Adding (iv), (v) and (iv), we get
` a (m-n) = b (n-l) + c (l-m)`
`= (ab-ac)/A + (bc-ab)/A + (ac - bc)/A =0` .