A body moves in a plane so that the displacements along the x and y axes are given by $x = 3 t^{3}$ and $y = 4 t^{3}$ . The velocity of the body is :

10 t

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15 t

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15 t^{2}

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25 t^{2}

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Solution

The correct option is C $15 t^{2}$
Given,

$x = 3 t^{3}$

$y = 4 t^{3}$

The velocity along x-axis, $v_{x} = \frac{d x}{d t} = 9 t^{2}$

The velocity along y-axis, $v_{y} = \frac{d y}{d t} = 12 t^{2}$

The velocity, $\to v = v_{x}^i + v_{y}^j$

$\to v = 9 t^{2}^i + 12 t^{2}^j$

The magnitude of the velocity, $| \to v | = \sqrt{(9 t^{2})^{2} + (12 t^{2})^{2}} = \sqrt{225 t^{4}}$

$| \to v | = 15 t^{2}$

The correct option is C.

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A body moves in a plane so that the displacements along the x and y axes are given by x=3t3 and y=4t3. The velocity of the body is :

The correct option is C 15t2Given,x=3t3y=4t3The velocity along x-axis, vx=dxdt=9t2The velocity along y-axis, vy=dydt=12t2The velocity, →v=vx^i+vy^j→v=9t2^i+12t2^jThe magnitude of the velocity, |→v|=√(9t2)2+(12t2)2=√225t4|→v|=15t2The correct option is C.

A body moves in a plane so that the displacements along the x and y axes are given by $x = 3 t^{3}$ and $y = 4 t^{3}$ . The velocity of the body is :