Question

. Suppose that the displacement of an object is related to time according to the expression: x(t) = B t3 . Using dimensional analysis, find the dimensionality of B.

Answer 1

Answer:

The dimensionality of B is length per cubic time.

Explanation:

Units for displacement and time are length $[L]$ and time $[T]$, respectively. Then, formula can be tested for dimensional analysis as follows:

$[L] = B\cdot [T]^{3}$

Now, let is clear $B$ to determine its units:

$B = \frac{[L]}{[T]^{3}}$

The dimensionality of B is length per cubic time.