• # question_answer A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a length$s={{t}^{3}}+5,$where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of P when$t=2s$ is nearly. [AIEEE 2010] A) $14\text{ }m/{{s}^{2}}$ B) $13\text{ }m/{{s}^{2}}$ C) $12\text{ }m/{{s}^{2}}$ D) $7.2\text{ }m/{{s}^{2}}$

 [a] $s={{t}^{3}}+5$ $v=\frac{ds}{dt}=3{{t}^{2}}$ $\frac{dv}{dt}=6t$ $a=\sqrt{(a_{r}^{2}+a_{t}^{2})}$$=\sqrt{{{\left( \frac{{{v}^{2}}}{R} \right)}^{2}}+{{\left( \frac{dv}{dt} \right)}^{2}}}=14\,m/{{s}^{2}}$ At $t=2s$