Question

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 = t³+5 , where s is in metre and t is in second . are radius of the path is 20m . the acceleration of P when t = 2s is nearly [ AIEEE 2010] ​

Answer 1

$s = {t}^{3} + 5$

$v = \frac{ds}{dt} = 3 {t}^{2}$

$and \: at = \frac{dv}{dt} = 6t$

$(at)t = 2 = 12$

aR =v^2/R =(Vt=2)^2/R

$a = \sqrt{a \times \frac{2}{t} } + \sqrt{a \times \frac{2}{r} } = 13.994$