The potential energy of particle of mass 5 kg moving in XY plane is given by equation U = (- 7x + 24y) J, where x and y are in meters. If particle starts its motion from origin then :
(i) magnitude of acceleration of particle is 5 m/s²
(ii) speed of particle at t = 5 s is 25 m/s
(iii) particle moves on parabolic path in XY-plane
(iv) particle moves on straight line in XY -plane

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(i, iii)

(ii, iv)

(i, ii, iv)

(i, iii, iv)

answer is A.

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Detailed Solution

$\vec{F} = - \frac{\partial U}{\partial X} \hat{i} - \frac{\partial U}{\partial Y} \hat{j} = 7 \hat{i} - 24 \hat{j} \Rightarrow | \vec{F} | = 25$
Magnitude of Acceleration $= \frac{F}{m} = \frac{25}{5} = 5 m / s^{2}$
Speed at t = 5s $\vec{v} = \vec{u} + \vec{a} t = \vec{0} + (\frac{7}{5} \hat{i} - \frac{24}{5} \hat{j}) (5)$
$= 7 \hat{i} - 24 \hat{j}$
Speed $= | \vec{v} | = 25 m / s$
As force = Constant and initially particle is at rest so particle moves on a straight line in XY-plane.