Question

S=A(1-e^-Bxt), where S is speed and x is displacement. What is the unit of B?​

Answer 1

Answer:

Unit of B = 1/ms

Dimensions of B = [L⁻¹T⁻¹]

Explanation:

Given

$S=A(1-e^{-Bxt})$

The power of e must be dimensionless quantity

Therefore the unit of B = 1/unit of xt

where x is displacement and t is time

Thus

the unit of B = 1/(unit of x × unit of t)

                    = 1/(metre × seconds)

                    = 1/m-s

The dimensions of B = 1/[LT] = [L⁻¹T⁻¹]

Hope it is helpful.