A body moves in a plane so that the displacement along the $X$ and $Y$ –axes is $x = 3 t^{2}$ and $y = 4 t^{2}$ , then velocity is

$15 t^{2}$

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$20 t^{2}$

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$5 t^{2}$

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None of these

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Solution

The correct option is D
None of these

Step 1. Given data
Displacement along $X$ axis, $x = 3 t^{2}$
Displacement along $y$ axis, $y = 4 t^{2}$
Step 2. Velocity of body
The velocity along $x -$ axis,
$V_{x} = \frac{d x}{d t} = \frac{d (3 t^{2})}{d t} = 6 t$
The velocity along $y$ -axis,
$V_{y} = \frac{d y}{d t} = \frac{d (4 t^{2})}{d t} = 8 t$
The velocity is, $\vec{v} = 6 t \hat{i} + 8 t \hat{j}$
Magnitude of velocity is
$|v| = \sqrt{{v_{x}}^{2} + {v_{y}}^{2}} = t \sqrt{6^{2} + 8^{2}} = 10 t$
Hence, option D is correct.

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Similar questions

x

y

x - y

A body moves in a plane, so that the displacement along $X$ and $Y - a x e s$ is $x = 3 t^{3}$ and $y = 4 t^{3}$ , then velocity is

x = 3 t^{3}

y = 4 t^{3}

x = 4 t^{2}; y = 3 t^{2}

x = 4 t + 4 t^{2}

y = 5 t

t = 1

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