Answer:
c) L³/T³
Explanation:
If t stands for time, the units are:
(V) = L³, (t) = T
The units for the equation:
V(t) = At³
must be:
[tex]L^{3} = \frac{L^{3} }{T^{3}} T^{3}[/tex]
If the volume of an object as a function of time is V(t) = At³, where A is a constant. Let L and T denote dimensions of length and time, respectively, then the dimension of the constant A would be L³ / T³, therefore the correct answer is the option C
A unit of measurement is a specified magnitude of a quantity that is established and used as a standard for measuring other quantities of the same kind. It is determined by convention or regulation. Any additional quantity of that type can be stated as a multiple of the measurement unit.
If t stands for time, the units are:
(V) = L³, (t) = T
The units for the equation:
V(t) = At³
Dimension of V = (Dimension of A) × (Dimension of t³)
L³ = dimension of A × T³
dimension of A = L³ / T³
Thus, If V(t) = At³, where A is a constant, then the volume of an object as a function of time. The dimension of the constant A would be L³ / T³, so the correct response is C if L and T stand for length and time dimensions, respectively.
Learn more about the unit of measurement from here
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