The coordinates of a moving particle at any time t is given by r- - at2 - - bt2 - The acceleration of the particle at any time is given by -

The correct option is C 2 √((a^2+b^2)) Here, x=at^2 and y=bt^2 Velocity components are, v_x=dxdt=2at and v_y=dydt=2bt Components of t ...

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Standard XII

Physics

Average Velocity in 2D Motion

The coordinat...

Question

The coordinates of a moving particle at any time $t$ is given by $\to r = a t^{2}^i + b t^{2}^j$ . The acceleration of the particle at any time is given by :

t^{2} \sqrt{(a^{2} + b^{2})}

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2 t \sqrt{(a^{2} + b^{2})}

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2 \sqrt{(a^{2} + b^{2})}

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Solution

The correct option is C $2 \sqrt{(a^{2} + b^{2})}$
Here, $x = a t^{2}$ and $y = b t^{2}$
Velocity components are, $v_{x} = \frac{d x}{d t} = 2 a t$ and $v_{y} = \frac{d y}{d t} = 2 b t$
Components of the acceleration are, $a_{x} = \frac{d v_{x}}{d t} = 2 a$ and $a_{y} = \frac{d v_{y}}{d t} = 2 b$
Thus, magnitude of the acceleration $= \sqrt{a_{x}^{2} + a_{y}^{2}} = \sqrt{(2 a)^{2} + (2 b)^{2}} = 2 \sqrt{a^{2} + b^{2}}$

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The coordinates of a moving particle at any time t is given by →r=at2^i+bt2^j. The acceleration of the particle at any time is given by :

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