Problem 1.3. Show that the expression S=Vit + 1/2at^2 is dimensionally correct, when S is a co-ordinate and has unit of length, vi is velocity, a is acceleration, and t is time.
Solution: Here x is the distance in meter, vo, is velocity in m/s, a is acceleration in m/s² and t is time in second. The dimensions of these physical quantities are:
x = Vot+ 1/2 at²
L=LT⁻¹ × T +LT⁻² × T²(·.· 1/2 is dimensionless quantity)
L=LT° +LT°
L=L+L (·.· T° = 1) ⇒ L = 2L ⇒ L=L
Since both sides of the equation have the same dimensions, therefore, the given equation is dimensionally correct.
