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 ?

Step-by-step solution

F → = - ∂ U ∂ x i ^ - ∂ U ∂ y j ^ = 7 i ^ - 24 j ^ ∴       a x = F x m = 7 5 = 1.4   m s - 2 along positive x -axis 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 - 2 and v y = 4.8 × 2 = 9.6   m s - 1 ∴   v = v x 2 + v y 2 = 10   m s - 1