Calculus Level 2

A particle is executing 1D motion. Its acceleration as a function of time is given by \(a=-Aw^{2}\sin(wt)\). At time \(t\), the magnitude of displacement from the mean position, velocity, acceleration are equal. Then find the value of \(t\).

Details and assumptions:

  • At maximum acceleration(magnitude), velocity is 0
  • At maximum velocity, displacement is zero
  • \(w\) is angular frequency
  • 'A' a is constant of appropriate dimensions

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