Question

s= A (1-e Bxt), Where S is speed, t is time and x is displacement. Then the dimensional formula of B is ?

Answer 1

Answer:

m^{-1}s^{-1}m−1s−1

Explanation:

it is given that, \bf{s=A(1-e^{Bxt})}s=A(1−eBxt) where S is speed , t is time , x is displacement.

we know,

unit of speed, s = metre/second

unit of time, t = second

unit of displacement , x = metre

from expression,

(1 - e^{bxt}) has neither unit nor dimension.

so, unit of power of exponential = 1

or, unit of Bxt = 1

or, unit of B × unit of x × unit of t = 1

or, unit of B × metre × second = 1

or, unit of B = 1/meter × second

.

hence, unit of B is m^{-1}s^{-1}m−1s−1 .