What is the dimensional consistency of s = Vot + 1/2 at2

The formula is dimensionally consistent

Explanation:

Dimensional Analysis

There are three fundamental magnitudes in Physics:

L = Length

T = Time

M = Mass

All the formulas and equations that use physical magnitudes must be consistent in their units.

For example, the formula:

Is used to calculate the distance traveled by an object, knowing its initial speed vo, acceleration a, and time t.

The units for each magnitude are:

s   = L

vo = L/T or

a   = L/T^2 or

Let's analyze the dimensions of the magnitudes in the formula (the constant 1/2 is neglected because it doesn't affect the dimensional analysis):

The first term simplifies to L because the T's simplify. The same happens with the second term, the squared T's simplify:

Thus the formula is dimensionally consistent

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach

80cm/s.

24cm/s.

53.3cm/s.