The particle has a mass of 0.36 kg. At point A, the speed of the particle is 6.1 m/s. Its kinetic energy at point B is 11.3 J.
The kinetic energy of a particle with mass m and moving at a speed v is given by K.E. = (1/2)*m*v^2
As the speed of the particle is 6.1 m/s at point A, its kinetic energy is (1/2)*0.36*(6.1)^2 = 6.6978 J
The kinetic energy of the particle at B is given as 11.3 J. If the speed of the particle at point B is v, (1/2)*0.36*v^2 = 11.3
=> v^2 = 2*11.3/0.36 = 565/9 m/s
=> v = 7.92 m/s.
The work done by the particle in moving from A to B is the difference in the energy of the particle at the two points. This is equal to 11.3 - 6.6978 = 4.6022. The work done by the particle in moving from A to B is 4.6022 J.