Prove the relation, `s_t=u + at - 1/2 a.`

Check the accuracy of the relation s = ut + (1)/(2)at^(2) where s is the distance travelled by the with uniform acceleration a in time t and having initial velocity u.

Check the correctness of the relation s_(t) = u+ (a)/(2) (2t-1) where u is initial velocity a is acceleration and s_(t) is the diplacement of the body in t^(th) second .

(a) Write a equation of motion in different states and derive the relation : s=u+(1)/(2)a(2t-1) Where, s is the distance covered in t^("th") second, u is initial velocity and a is uniform acceleration.

Derive dimensionally the relation s = ut +(1)/(2)f t^(2) .

Chek the correctness of the relation, S_(nth) = u +(a)/(2)(2n -1), where u is initial velocity, a is acceleratin and S_(nth) is the distance travelled by the body in nth second.

Chek the correctness of the relation, S_(n_(th)) = u +(a)/(2)(2n -1), where u is initial velocity, a is acceleratin and S_(n_(th)) is the distance travelled by the body in nth second.