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 $[0 \leq t \leq 1]$ . If $α$ denotes the instantaneous acceleration of the particle, then

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$|\begin{matrix} α \end{matrix}|$ cannot exceed $2$ at any point in its path

$α$ cannot remain positive for all $t$ in the interval $0 t o 1$

α | must be ≥ 4 at some point or points in its path

α must change sign during the motion, but no other assertion can be made with the given information.

answer is A, C.

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Detailed Solution

For the data, $\underset{v}{\to} - t$ graph can be drawn as shown in the figure . The displacement in time $t$ ,

x = \frac{1}{2} (\frac{α β}{α + β}) t^{2} x = 1, t = 1 s α = β α = 4, α > β α > 4 m / s^{2}

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