Question

CHeck the dimantion consistance v=u+At?

Answer 1

To check the dimensional correctness of a given physical relation, we should check whether the dimensions on both sides of each term is the same or not, if not the equation is dimensionally incorrect; if the dimensions on both sides of each term of the give equation are same the given equation is dimensionally correct.
 
Example:

To check the correctness of v = u + at, using dimensions
Dimensional formula of final velocity v = [LT-1]
Dimensional formula of initial velocity u = [LT-1]
Dimensional formula of acceleration x time, at = [LT-2 x T]
= [LT-1]

Answer 2

equation is v=u+at
dimensional formula of v = (M°LT^-1)
dimensional formula of u = (M°LT^-1)
dimensional formula of a = (M°LT^-2)
dimensional formula of t = (M°L°T)
LHS is the dimensional formual of v=(M°LT^-1)
RHS=dimensional formula of u+dimensional formula of a×dinensional formula of t
=(M°LT^-1)+(M°LT^-2)×(M°L°T)
=(M°LT^-1)+(M°LT^-1)
=2(M°LT^-1)
2 is a dimensionless constant,therefore LHS=RHS
hence,the given relationship is dimensionally correct...