Question

Show that Vf=Vi +at is dimensionaly correct.​

Answer 1

Answer:

$\bullet \: \bold{LHS} = \sf V_{final} = velocity$

$\longrightarrow\: \underline{ \boxed{\sf [V_{final}] =[M^0L^1T^{-1}]}}$

$\bullet \: \bold{RHS} = \sf V_{initial} = velocity$

$\longrightarrow\: \underline{ \boxed{\sf [V_{final}] =[M^0L^1T^{-1}]}}$

And,

$\bullet \: \bold{RHS} = \sf at= acceleration \times time$

$\longrightarrow\: \sf [at] = [M^0L^1T^{-2}][T ^{1} ]$

$\longrightarrow\: \underline{ \boxed{\sf [at] = [M^0L^1T^{-1}]}}$

As, LHS = RHS , Formula is Dimensionally correct.