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, then

The first part of the motion must be accelerated motion and the second part must be retarded motion .

If the average value of magnitude of acceleration in the first part and second part of its journey be $\left|\alpha \right| and maximum velocity be v , then \frac{2v}{\left|\alpha \right|}=1..............\left(1\right) and \frac{v^2}{\left|\alpha \right|}=1.....\left(2\right)$

Solving , $\left|\alpha \right|=4.So if \alpha is variable , at some point or points \left|\alpha \right|\ge 4.$