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A vehicle is moving on a road of grade $+4 \%$ at a speed of $20 \: m/s$. Consider the coefficient of rolling friction as $0.46$ and acceleration due to gravity as $10 \: m/s^2$. On applying brakes to reach a speed of $10 \: m/s$, the required braking distance (in m, round off to nearest integer) along the horizontal, is ______
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