The force f =fi^ on a particle of mass 2 kg moving along the x axis is given in the fig as a function of its position x; the particle is moving with a velocity of 5m/s along the x axis at x =0 what is the kinetic energy of the particle at x=8

Initial velocity along X axis, U_x = 5 m/s

Acceleration upon the action of force = F cos θ / mass

= 10 √2 x (1/√2) / 2

= 10/2

= 5 m/s².

 Now, V_x = U_x + a_xt

V_x = 5 + [5 x 3] 

V_x = 20m/s

Now, displacement alonf Y axis also needs to be considered as the force will displace the body from its straight line path.

So, V_y = U_y + a_yt

V_y = 0 + 5 x 3 = 15 m/s

Now, resultant V = √(V_x²  + V_y²)

= √(20² + 15²)

Thus,velocity after 3 sec = 25 m/s.