A particle of mass m moves on the x-axis as f | vedclass

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(D) The particle starts from rest at $x = 0$ ($v = 0$ at $t = 0$) and comes to rest at $x = 1$ ($v = 0$ at $t = 1$).Since the particle moves from $x =

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Both $(a)$ and $(c)$

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(D) The particle starts from rest at $x = 0$ ($v = 0$ at $t = 0$) and comes to rest at $x = 1$ ($v = 0$ at $t = 1$).Since the particle moves from $x = 0$ to $x = 1$,its average velocity is positive. For the particle to start from rest and end at rest,it must accelerate initially to gain velocity and decelerate later to come to a stop.If $\alpha$ remained positive for the entire interval $0 \le t \le 1$,the velocity would be strictly increasing,meaning the particle could not return to rest at $t = 1$.Therefore,$\alpha$ cannot remain positive for all $t$ in the interval $0 \le t \le 1$,which implies $\alpha$ must change sign during the motion.Thus,both statements $(a)$ and $(c)$ are correct.

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