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The potential energy of a particle of mass 5kg moving in the xy plane is given as $U = - 7x + 24y$ joules x and y in meters. Initially at t=0 the particle is at origin (0, 0) moving with a velocity of $\vec{v} = 6 [2.4 \hat{i} + 0.7 \hat{j}] m / s$ then

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The magnitude of velocity of the particle at t= 4sec is nearly 25m/s

The direction of motion of the particle initially at t=0 is at right angles to the direction of acceleration

The magnitude of acceleration of the particle is $5 m / s^{2}$

The path of the particle is circle

answer is A, B, C.

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Detailed Solution

$\vec{F} = 7 \hat{i} - 24 \hat{j}, \vec{a} = \frac{7}{5} \hat{i} - \frac{24}{5} \hat{j}, v_{(t = 4)} = 20 \hat{i} - 15 \hat{j}$

by using equation of motion $\vec{v} ⊥ \vec{a}$ not always as $\vec{a}$ is constant However initially $\vec{v} . \vec{a} = 0$

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