Question

Dimantional correct check s=v+1/2at^2​

Answer 1

Explanation:

Dimensional check for correctness of equation

$s = v + \frac{1}{2} a {t}^{2} \\ now \\ [s] = [v] + [a {t}^{2} ] \\ [ {M}^{o} {L}^{1} {T}^{o} ] = [ {M}^{o} {L}^{1} {T}^{ - 1} ] = [ {M}^{o} {L}^{1} {T}^{ - 2} ][ {M}^{o} {L}^{0} {T}^{2} ] \\ {M}^{o} {L}^{1} {T}^{o} ] = [ {M}^{o} {L}^{1} {T}^{ - 1} ] = [ {M}^{o} {L}^{1} {T}^{ o} ]$

Dimension for s and at^2 are correct but for v is not. Hence the equation is not correct

$the \: equation \\ s = vt + \frac{1}{2} a {t}^{2} \\ is \: dimensionally \: correct$