JEE Advance - Physics (1993 - No. 1)
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 come 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:
$$\alpha $$ cannot remain positive for all t in the interval $$0 \le t \le 1$$
$$\left| \alpha \right|$$ cannot exceed 2 at any point in its path.
$$\left| \alpha \right|$$ must be $$ \ge $$ 4 at some point or points in its path.
$$\alpha $$ must be change sign during the motion, but no other assertion can be made with the information given.