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2.Motion in Straight Line
medium
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...........$m/s^2$
A
$24$
B
$0$
C
$6$
D
$12$
(AIPMT-2012)
Solution
$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Give\,:\,x = 8 + 12t – {t^3}\\
\,velocity\,,\,v = \frac{{dx}}{{dt}} = 12 – 3{t^2}\\
When\,v = 0,\,12 – 3{t^2} = 0\,\,\,or\,\,t = 2\,s\\
\,\,\,\,\,\,\,\,\,\,\,a = \frac{{dv}}{{dt}} = – 6t\\
\,\,\,\,\,\,\,\,\,\,\,a\left| {_{t = 2\,s} = – 12\,m\,{s^{ – 2}}} \right.\\
{\rm{Retardation}}\, = 12\,m\,{s^{ – 2}}
\end{array}$
Standard 11
Physics
