• # question_answer 8) A particle leaves the origin with an initial velocity$\vec{v}=3\hat{i}\,m/s$and a constant acceleration $\vec{a}=(\hat{i}0.5\hat{j})\,m/{{s}^{2}}$When the particle reaches its maximum$x-$coordinate, what is its $y-$component of velocity? A) $~-2.0\text{ }m/s$                B) $-1.0\text{ }m/s$C) $-1.5\text{ }m/s$                   D) $~1.0\text{ }m/s$

Solution :

The $x-$component of velocity ${{v}_{x}}={{v}_{ax}}+{{a}_{x}}t=3-t\,m/s.$ The y- component is ${{v}_{y}}={{v}_{ay}}+{{a}_{y}}t=-0.5t\frac{m}{s},$when the particle reaches its maximum$x-$coordinate, ${{v}_{x}}=0,$or $t=3\sec .$ The$y-$component of the velocity at this time is ${{v}_{y}}=-0.5\times 3=-1.5\,m/s$ Hence, the correction option is [c].

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