Question

Show that the expression s=vit+ ½at² is dimensionally correct

Answer 1

Equation:

$\sf { s = v_{i} t + \frac{1}{2} a t^{2} }$

Dimensions:

s = [L]

vi = [L/T]

a = [LT^-2]

t = [T]

1/2 = Dimensionless

=> [L] = [LT^-1] [T] + [LT^-2] [T^2]

=> [L] = [L] + [L]

=> [L] = [L]

hence proved.