A particle of mass \( m \) moves on the \( x \)-axis as follows : it starts from rest at \( t=0 ...

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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 math xmlns=http://www.w3.org/1998/Math/MathMLmo(/momn0/mnmo</momit/mimo</momn1/mnmo)/mo/math. If math xmlns=http://www.w3.org/1998/Math/MathMLmiα/mi/math denotes the instantaneous acceleration of the particle, then
(a) \( \alpha \) cannot remain positive for all \( t \) in the interval \( 0 \leq t \leq 1 \)
(b) \( |\alpha| \) cannot exceed 2 at any point in its path
(c) \( |\alpha| \) must be \( \geq 4 \) at some point or points in its path
(d) \( \alpha \) must change sign during the motion, but no other assertion can be made with the information given
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