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

The dimensionality of B is length per cubic time.

Step-by-step 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 = ([L])/([T]^(3))`

The dimensionality of B is length per cubic time.