Check the correctness of following equation by the method of dimensions :
`S=ut+(1)/(2)at^(2)` .
where S is the distance covered bu a body in time t, having initial velocity u and acceleration a.

Check the correctness of the following equation by the method of dimensions. s=ut+1/2at^2

Check the correctness of the following equation by the method of dimensions (i) v^(2)=u^(2)+2gs (ii) s=ut+1/2"gt"^(2) (iii) v=u+"gt"

Derive an expression using the method of dimensions, the distance travelled by a body during an interval of time t, if its initial velocity is u and uniform acceleration is 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 following equation using dimensional analysis. Make a comment on it. S = ut + 1//2 "at"^(2) where s is the displacement, u is the initial velocily, t is the time and a is the acceleration produced,

(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.

Check the correctness of the equations, (i) s = ut + 1//2 at ^ 2 and (ii) s _ (nth) = u + (a)/(2) ( 2 n - 1 )