A car is moving with a speed of $30 m / s$ on a circular path on a radius $500 m$ . It is increasing at the rate of $2 m / s e c^{2}$ . What is the acceleration of the car?

9.8 m / s e c^{2}

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2.7 m / s e c^{2}

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2.4 m / s e c^{2}

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1.8 m / s e c^{2}

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Solution

The correct option is B $2.7 m / s e c^{2}$
Total acceleration= $\sqrt{a_{c}^{2} + (l i n e a r)^{2}}$
angular= $a_{c} = ω^{2} R = \frac{v^{2}}{R} = \frac{900}{500} = \frac{9}{5}$
Total acceleration= $\sqrt{\frac{81}{25} \times 4}$
$= \sqrt{\frac{181}{25}}$
$= 2.7 m / s^{2}$

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A car is moving with a speed of 30m/s on a circular path on a radius 500m. It is increasing at the rate of 2m/sec2. What is the acceleration of the car?

The correct option is B 2.7m/sec2Total acceleration=√a2c+(linear)2angular=ac=ω2R=v2R=900500=95Total acceleration=√8125×4=√18125=2.7m/s2

A car is moving with a speed of $30 m / s$ on a circular path on a radius $500 m$ . It is increasing at the rate of $2 m / s e c^{2}$ . What is the acceleration of the car?

The correct option is B $2.7 m / s e c^{2}$
Total acceleration= $\sqrt{a_{c}^{2} + (l i n e a r)^{2}}$
angular= $a_{c} = ω^{2} R = \frac{v^{2}}{R} = \frac{900}{500} = \frac{9}{5}$
Total acceleration= $\sqrt{\frac{81}{25} \times 4}$
$= \sqrt{\frac{181}{25}}$
$= 2.7 m / s^{2}$