Source: Extra Practice
The displacement of a particle is given by x = at + bt², where x is in meters and t is in seconds. The units of 'b' are:
Options
Option A is correct
m/s²
Option B
m/s
Option C
m s
Option D
m
Explanation
By the principle of homogeneity, dimensions of each term on the RHS must equal dimensions of the LHS. So, [bt²] = [x]. [b] [T²] = [L]. Thus, [b] = [L T⁻²]. The unit is meters per second squared (m/s²). m/s is the unit for 'a', m s and m are dimensionally inconsistent with the term bt² equaling a length.