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Uniform and Non Uniform

A car is trav...

Question

A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of $a m / s^{2}$ , then the resultant acceleration will be

(\frac{v^{2}}{r} + a)

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{(\frac{v^{2}}{r^{2}} + a)}^{1 / 2}

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{(\frac{v^{4}}{r^{2}} + a^{2})}^{1 / 2}

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{(\frac{v^{2}}{r^{2}} - a^{2})}^{1 / 2}

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Solution

The correct option is A ${(\frac{v^{4}}{r^{2}} + a^{2})}^{1 / 2}$
Radial acceleration $a_{r} = \frac{v^{2}}{r}$
tangential acceleration $a_{t} = a$
$a_{n e t} = (a_{r}^{2} + a_{t}^{2})^{\frac{1}{2}} = (\frac{v^{4}}{r^{2}} + a^{2})^{\frac{1}{2}}$

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A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of a m/s2, then the resultant acceleration will be

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A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of $a m / s^{2}$ , then the resultant acceleration will be

The correct option is A ${(\frac{v^{4}}{r^{2}} + a^{2})}^{1 / 2}$
Radial acceleration $a_{r} = \frac{v^{2}}{r}$
tangential acceleration $a_{t} = a$
$a_{n e t} = (a_{r}^{2} + a_{t}^{2})^{\frac{1}{2}} = (\frac{v^{4}}{r^{2}} + a^{2})^{\frac{1}{2}}$