Question

Prove that the equation,v=u+at,is dimensionally correct

Answer 1

Explanation:

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.