Question

Which of the following equations are dimensionally consistent?

(a) x=1/2at2,
(b) t=v/x,
(c) t=(2x/a)1/2

Answer 1

A. x = 1/2at²

Explanation:

Among the equations, the equation that is dimensionally consistent is x=1/2at² where;

x is the distance in meters (dimension is length (L))

a is the acceleration in m/s² (dimension is L/T²)

t is the time in seconds (s) (dimension of time is T)

Substituting the dimensions into the formula to check if we are going to arrive at the dimension for distance;

1/2at² = 1/2(L/T²)T²

= 1/2× L/T² × T²

= 1/2 × L

Since L which is the resulting dimension is the dimension for distance (x), this means that the equation x = 1/2at² is dimensionally consistent.