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 , where x and y are given in metre. If the particle starts from rest, from the origin, then the speed of the particle at t = 2 s is

Question

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 , where x and y are given in metre. If the particle starts from rest, from the origin, then the speed of the particle at t = 2 s is, 5 m/s, 14 m/s, 17 .5 m/s, 10 m/s

MARKS App · Accepted Answer

F = - ∂ U ∂ x i ^ - ∂ U ∂ y j ^ = 7 i ^ - 24 j ^ ∴ a x = F x m ⁡ = 7 5 = 1.4 m/s 2 a y = F y m ⁡ = - 24 5 = 4.8 m/s 2 along negative y − axis ​ ∴ v ⁡ x = a x t ⁡ = 1.4 × 2 = 2.8 m/s along negative y − axis and v ⁡ y = 4.8 × 2 = 9.6 m/s ∴ v ⁡ = v ⁡ x 2 + v ⁡ y 2 = 10 m/s

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