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(C) particle is at rest when its velocity is zero. In terms of position-time graphs,this means the slope of the graph (which represents velocity) must

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$2 - 3\ s$

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(C) particle is at rest when its velocity is zero. In terms of position-time graphs,this means the slope of the graph (which represents velocity) must be zero,implying the position remains constant over that time interval.Looking at the $x-t$ graph,the position $x$ is constant (a horizontal line) between $t = 2\ s$ and $t = 3\ s$.Looking at the $y-t$ graph,the position $y$ is constant (a horizontal line at $y = 0$) between $t = 1\ s$ and $t = 3\ s$.For the particle to be at rest in two dimensions,both its $x$ and $y$ components of velocity must be zero simultaneously.Therefore,the particle is at rest during the interval where both graphs are horizontal,which is between $t = 2\ s$ and $t = 3\ s$.

During which time interval is the particle described by these position graphs at rest?

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