# 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/s^{2}.

Now, V_{x} = U_{x} + a_{x}t

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_{y}t

V_{y} = 0 + 5 x 3 = 15 m/s

Now, resultant V = √(V_{x}^{2} + V_{y}^{2})

= √(20^{2} + 15^{2})

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