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A point moves along a circle with a velocity $v = \frac{t}{2}$ . Find the acceleration of the point at the moment when it has covered a quarter circle from the beginning of motion.

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$\frac{1}{2} \sqrt{π^{2} + 1}$

$\sqrt{π^{2} - 1}$

$\frac{1}{2} \sqrt{π^{2} - 1}$

$\sqrt{π^{2} + 1}$

answer is A.

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Detailed Solution

$a = \sqrt{a_{c}^{2} + a_{t}^{2}} H e r e a_{c} = \frac{v^{2}}{R} a_{t} = \frac{d v}{d t} S = u t + \frac{1}{2} a_{t}^{2} t^{2} \frac{π r}{2} = 0 + \frac{1}{2} \times \frac{1}{2} \times t^{2} a = \frac{1}{2} \sqrt{π^{2} + 1}$

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