A particle of mass m is constrained to move o | vedclass

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(D) The particle starts from rest at $x=-A$. The acceleration is $a = F/m$ towards the right.Let $t_1$ be the time taken to travel from $x=-A$ to $x=0

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$\sqrt{\frac{ m A }{ F }}(\sqrt{2}-1)$

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(D) The particle starts from rest at $x=-A$. The acceleration is $a = F/m$ towards the right.Let $t_1$ be the time taken to travel from $x=-A$ to $x=0$. Using $s = ut + \frac{1}{2}at^2$ with $u=0$ and $s=A$:$A = 0 + \frac{1}{2} (F/m) t_1^2 \implies t_1 = \sqrt{\frac{2mA}{F}}$.Let $t_2$ be the time taken to travel from $x=-A$ to $x=-A/2$. Using $s = A/2$:$A/2 = 0 + \frac{1}{2} (F/m) t_2^2 \implies t_2 = \sqrt{\frac{mA}{F}}$.The time taken to travel from $x=-A/2$ to $x=0$ is $\Delta t = t_1 - t_2$.$\Delta t = \sqrt{\frac{2mA}{F}} - \sqrt{\frac{mA}{F}} = \sqrt{\frac{mA}{F}}(\sqrt{2}-1)$.

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