A car accelerates from rest at a constant rate $4 m / s^{2}$ for sometime after which it deaccelerates at constant rate $3 m / s^{2}$ to come to rest. If total time is 14s then average speed of car is

12 m/s

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6 m/s

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24 m/s

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3 m/s

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Solution

The correct option is A 12 m/s

Let the car accelerate for $^{'} t_{1}^{'}$ s and decelerate for $(14 - t_{1}) s$
$v = 4 t_{1}$
Also, $0 = 4 t_{1} - 3 (14 - t_{1}) \to 4 t_{1} = 42 - 3 t_{1} ∴ t_{1} = 6$
$A v e r a g e s p e e d = \frac{\frac{1}{2} \times 14 \times 24}{14} = 12 m / s$ .

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