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A particle moves in a circle of radius 20cm. Its linear speed is given by $v = 2 t$ , where ' $t$ ' is in second and ' $v$ ' in m/s. The radial and tangential acceleration at $t = 3 s$ respectively are

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$180 m / s^{2}, 2 m / s^{2}$

$160 m / s^{2}, 1 m / s^{2}$

$190 m / s^{2}, 3 m / s^{2}$

$170 m / s^{2}, 4 m / s^{2}$

answer is A.

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Detailed Solution

At $t = 3 \sec$ $V = 2 (3) = 6 m / s a_{r} = \frac{v^{2}}{r} = 180 m / s^{2} a_{t} = \frac{d v}{d} = \frac{d}{d t} (2 t) a_{t} = 2 m / s^{2}$

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