# 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 $$K$$.

×