A particle moves along the x-axis such that its position x(t) = t³ − 6t² + 9t + 5. The time when the particle is momentarily at rest is: A. t = 1 and t = 3 B. t = 2 and t = 4 C. t = 1 and t = 2 D. t = 3 and t = 5 Answer: A) t = 1 and t = 3 Explanation: Velocity v = dx/dt = 3t² − 12t + 9 = 3(t² − 4t + 3) = 3(t − 1)(t − 3). v = 0 at t = 1 and t = 3.

imo class 12 application of derivatives

A particle moves along the x-axis such that its position x(t) = t³ − 6t² + 9t + 5. The time when the particle is momentarily at rest is:

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A particle moves along the x-axis such that its position x(t) = t³ − 6t² + 9t + 5. The time when the particle is momentarily at rest is:

Answer: A) t = 1 and t = 3

Explanation: Velocity v = dx/dt = 3t² − 12t + 9 = 3(t² − 4t + 3) = 3(t − 1)(t − 3). v = 0 at t = 1 and t = 3.