The volume of an object as a function of time is calculated by v = At3+B:t where t is time measured in seconds and v is in cubic metres. Determine the dimension of the constants A and B.

A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

B = m³s = [L³T]

Explanation:

We have the equation:

V = At³ + B/t

where, the dimensions of each variable are as follows:

V = m³ = [L]³

t = s = [T]

substituting these in equation, we get:

m³ = A (s) ³ + B/s

for the homogeneity of the equation:

A (s) ³ = m³

A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

Also,

B/s = m³

B = m³s = [L³T]