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PhysicsW.E.P.Conservative force & potential energyMedium2 minPYQ_2020

PhysicsMediumnumerical

The potential energy of a particle of mass $5 kg$ moving in the $x - y$ plane is given by $U = (- 7 x + 24 y) J$ , $x$ and $y$ being in $metre$ . If the particle starts from rest from origin, then what is the speed (in $m s^{- 1}$ ) of particle at $t = 2 s$ ?

Answer:

10.00

Solution:

$\vec{F} = - \frac{\partial U}{\partial x} \hat{i} - \frac{\partial U}{\partial y} \hat{j} = 7 \hat{i} - 24 \hat{j}$

$∴ a_{x} = \frac{F_{x}}{m} = \frac{7}{5} = 1.4 m s^{- 2}$ along positive $x$ -axis

$a_{y} = \frac{F_{y}}{m} = - \frac{24}{5}$

$= 4.8 m s^{- 2}$ along negative $y$ -axis

$∴ v_{x} = a_{x} t = 1.4 \times 2$

$= 2.8 m s^{- 2}$

and $v_{y} = 4.8 \times 2 = 9.6 m s^{- 1}$

$∴ v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 10 m s^{- 1}$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Conservative force & potential energy

⏱ 2mℹ️ Source: PYQ_2020

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