The distance moved by a particle travelling in straight line in t seconds is given by s = 45t + 11t2 − t3. The time taken by the particle to come to rest is

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9 sec s = 45t + 11 t^2 - t^3 \Rightarrow ds/dt = 45 + 22t - 3 t^2 	ext { According to the question,} 3 t^2 - 22t - 45 = 0 \Rightarrow 3 t^2 - 27t + 5t - 45 = 0 \Rightarrow 3t\left( t - 9 ight) + 5\left( t - 9 ight) = 0 \Rightarrow \left( t - 9 ight)\left( 3t + 5 ight) = 0 \Rightarrow \left( t - 9 ight) = 0 	ext { or } \left( 3t + 5 ight) = 0 	ext { As time can't be negative }, t = 9 \sec

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