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Non Uniform Motion & Avg Velocity

A particle mo...

Question

A particle moves on the curve y = $\frac{x^{2}}{4}$ where x = $\frac{t}{2}$ . x and y are measured in metre and t in second. At t = $4$ s, the velocity of particle is

\frac{1}{\sqrt{2}}

m/s

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\sqrt{3}

m/s

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\sqrt{2}

m/s

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2 \sqrt{2}

m/s

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Solution

The correct option is A $\frac{1}{\sqrt{2}}$ m/s
The x co-ordinate is given as $x = \frac{t}{2}$
Thus velocity component in x direction $v_{x} = \frac{d x}{d t} = \frac{1}{2} m / s$
The y co-ordinate is given as $y = \frac{x^{2}}{4} = \frac{t^{2}}{16}$
Thus velocity component in y direction $v_{y} = \frac{d y}{d t} = \frac{2 t}{16} = \frac{t}{8} m / s$
At $t = 4 s,$ $v_{y} = \frac{4}{8} = \frac{1}{2} m / s$
So, net velocity $V = \sqrt{v_{x}^{2} + v_{y}^{2}}$
$⟹ V = \sqrt{(\frac{1}{2})^{2} + (\frac{1}{2})^{2}} = \frac{1}{\sqrt{2}} m / s$

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A particle moves on the curve y = x24 where x = t2. x and y are measured in metre and t in second. At t = 4s, the velocity of particle is

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