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A particle is...

Question

A particle is moving on a circular track of radius 4 m with speed $v = t^{2} - t + 2$ . Find the acceleration of particle at t = 2 sec. ___

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Solution

$a_{t} = \frac{d v}{d t} = 2 t - 1$
$a_{t} = 2 (2) - 1 = 3 m / s^{2}$
$a_{c} = \frac{v^{2}}{R} = \frac{(4 - 2 + 2)^{2}}{4} = 4 m / s^{2}$
$a = \sqrt{3^{3} + 4^{2}} = 5 m / s^{2}$

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