The particle has an initial velocity of 9.1 m/s in the positive x-direction. It is accelerated at 5 m/s^2 in the positive y-direction for 6 s. Due to the acceleration the final velocity of the particle has a component in the direction of the positive x-axis of 9.1 m/s and a component in the direction of the positive y-axis of 5*6 = 30 m/s.
The final speed of the particle is the magnitude of its final velocity. This is the sum of the components of its velocity in the x and y axes which is equal to sqrt(30^2 + 9.1^2) = sqrt(900 + 82.81) = sqrt(982.81) = 31.34 m/s
The final speed of the particle is 31.34 m/s