A classical mechanics problem by Nitin Sachan

A particle of mass \(m\) moves on the \(x\)-axis as follows:

  • It starts from rest at \(t=0 \) from the point \(x=0 \) and comes to rest at \(t=1\) at the point \(x=1\).
  • No other information is available about its motion at intermediate times \((0<t<1) \).
  • If \(\alpha\) denotes the instantaneous acceleration of the particle.
  • It is given that at some point or points in the path \( |\alpha | \geq K \), where \(K \) is a natural number.

Compute \(K \).

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