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, Ux = 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, Vx = Ux + axt

V= 5 + [5 x 3] 

Vx = 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, Vy = Uy + ayt

Vy = 0 + 5 x 3 = 15 m/s

Now, resultant V = √(Vx2  + Vy2)

= √(202 + 152)

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

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