Question

using method of dimensions check the correctness of equation V = u+at​

Answer 1

Answer:

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

of a×dimensional formula of t=(M°LT^-1)+(M°LT^-2)×(M°L°T)

of a×dimensional formula of t=(M°LT^-1)+(M°LT^-2)×(M°L°T)=(M°LT^-1)+(M°LT^-1)

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. 

HOPE IT HELPS YOU.

Answer 2

Answer:

for correct dimensions at should have same dimensions as u

so

dimensionally at= m/s^2 * s = m/s

which is dimensionally equal to u and v