$A$ 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 time $(0 < t < 1)$. If $\alpha$ denotes the instantaneous acceleration of the particle,then

• A
  $\alpha$ cannot remain positive for all $t$ in the interval $0 \le t \le 1$
• B
  $|\alpha|$ cannot exceed $2$ at any point in its path
• C
  $\alpha$ must change sign during the motion but no other assertion can be made with the information given
• D
  Both $(a)$ and $(c)$