A car is moving with speed $27 k m / h$ . The driver applied brakes as he approaches a circular turn on the road of radius $80 m$ and his speed reduces at the constant rate of $0.50 m / s$ every second. The magnitude of net acceleration is

20 {m s}^{- 2}

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0.86 {m s}^{- 2}

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100 {m s}^{- 2}

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None of these

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Solution

The correct option is B $0.86 {m s}^{- 2}$
Speed $v = 27 k m / h r = 27 \times \frac{5}{18} = 7.5 m / s$
Radius of circular turn $r = 80 m / s$
Radial acceleration $a_{r} = \frac{v^{2}}{r} = \frac{{7.5}^{2}}{80} = 0.7 m / s^{2}$
Tangential acceleration $a_{t} = \frac{d V}{d t} = 0.50 m / s^{2}$
Net acceleration $a_{n e t} = \sqrt{a_{r}^{2} + a_{t}^{2}} = \sqrt{{0.7}^{2} + {0.5}^{2}} = 0.86 m / s^{2}$
Correct answer is option B.

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