The potential energy of a particle of mass \( 5 \mathrm{~kg} \) moving in \( x y \)-plane is giv...

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The potential energy of a particle of mass \( 5 \mathrm{~kg} \) moving in \( x y \)-plane is given as \( U=(7 x+24 y) \) joule, \( x \) and \( y \) being in metre. Initially at \( t=0 \), the particle is at the origin \( (0,0) \) moving with a velocity of \( (8.6 \hat{\mathbf{i}}+23.2 \hat{\mathbf{j}}) \mathrm{ms}^{-1} \). Then,
(a) the velocity of the particle at \( t=4 \mathrm{~s} \), is \( 5 \mathrm{~ms}^{-1} \)
(b) the acceleration of the particle is \( 5 \mathrm{~ms}^{-2} \)
(c) the direction of motion of the particle initially (at \( t=0 \) ) is at right angles to the direction of acceleration
(d) the path of the particle is circle
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