Q. The motion of a particle along a straight line is described by equation : $x = 8 + 12t - t^{3}$ Where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is
A) $24ms^{- 2}$
B) Zero
C) $6ms^{- 2}$
D) $12ms^{- 2}$
Explanation
(d) $x = 8 + 12t + t^{3}$
$v = 0 + 12 - 3t^{2} = 0$
$3t^{2} = 12$
$t = 2\ sec$
$a = \frac{dv}{dt} = 0 - 6t$
$a\lbrack t = 2\rbrack = - 12\ m/s^{2}$
Retardation $= 12\ m/s^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.