Question

Cheak the correctness of equation V=u+at by using dimension

Answer 1

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 formula of v=(M°LT^-1)
RHS=dimensional formula of u+dimensional formula of a×dimensional 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(equation)is dimensionally correct.