Q. A particle moves a distance $x$ in time $t$ according to equation $x = (t + 5)^{- 1}$. The acceleration of particle is proportional to
A) $(Velocity)^{2/3}$
B) $(Velocity)^{3/2}$
C) $(distance)^{2}$
D) $(distance)^{- 2}$
Explanation
(b) $x = \frac{1}{t + 5} \Rightarrow v = \frac{dx}{dt} = - \frac{1}{(t + 5)^{2}}$
Acceleration, $a = \frac{dv}{dt} = \frac{2}{(t + 5)^{3}} \Rightarrow a \propto (velocity)^{3/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.