A car enters a curved road in the form of a quarter of a circle, the path length being 200 metre .Its speed at the entrance is 18 kmh^-1 but when it leaves, it increases to 54 kmh^-1. If the car is travelling with constant acceleration along the curve, the acceleration when the car leaves the curved road is

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0.9 ms^-2

1.9 ms^-2

0.45 ms^-2

3.68 ms^-2

answer is C.

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Detailed Solution

$\begin{array}{l} a_{T} = \frac{v^{2} - u^{2}}{2 ℓ} = \frac{(15)^{2} - (5)^{2}}{2 (200)} = 0 .5 {ms}^{- 2} \\ a_{C} = \frac{v_{final}}{r} = \frac{(15)^{2}}{(\frac{400}{π})} \{∵ l = \frac{2 πr}{4} = 200\} \\ \Rightarrow a_{C} = 1 .8 {ms}^{- 2} \\ \Rightarrow a = \sqrt{(1 .8)^{2} + (0 .5)^{2}} \\ \Rightarrow a = 1 .9 {ms}^{- 2} \end{array}$

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