Two cars left place A simultaneously and reached the place B in 2 hrs. The first car travelled half the distance with a speed of $30 km/hr$ and the other half at a speed of $45 km/hr$ . The second car at the same time covered the entire distance with a constant acceleration starting from rest. Find the acceleration of the second car.

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36 {km/hr}^{2}

144 {km/hr}^{2}

72 {km/hr}^{2}

18 {km/hr}^{2}

answer is A.

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Detailed Solution

for both cars time is same

For car A :

$t = 2 hrs$

$v_{avg} = \frac{{2v}_{1} v_{2}}{v_{1} + v_{2}}$

$v_{1} = 30 kmph$

$v_{2} = 45 kmph$

$= \frac{2 \times 30 \times 45}{30 + 45}$

$= \frac{90 \times 30}{75}$

$= \frac{9 \times 100}{25} = 36 kmph$

$s = v_{a v g} \times t = 36 \times 2 = 72 km$

For car B :

$u = 0,s = 72 km, t = 2hr, a = ?$

$s = u + \frac{1}{2} {at}^{2}$

$72 = (0) (2) + \frac{1}{2} (a) {(2)}^{2}$

$72 = 0 + 2 a$

$\Rightarrow 2a = 72$

$\Rightarrow a = 36 {km/hr}^{2}$

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