Q. The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\left\lbrack 1 - e^{- bt} \right\rbrack.$ Then the velocity of the particle is
A) $k(e^{- bt})$
B) $\frac{k}{b^{2}e^{- bt}}$
C) $k\ b\ e^{- bt}$
D) None of these
Explanation
(a) $v = \frac{dx}{dt} = \frac{d}{dt}\left\lbrack \frac{k}{b}\left( 1 - e^{- bt} \right) \right\rbrack = \frac{k}{b}\left\lbrack 0 - ( - b)e^{- bt} \right\rbrack = ke^{- bt}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.