The change in kinetic energy is [tex]\Delta K = 3Fd[/tex]
Explanation:
According to the work-energy theorem, the work done on an object is equal to the change in kinetic energy of the object. Mathematically:
[tex]W=K_f -K_i= \Delta K[/tex]
where :
W is the work done on the object
[tex]K_f[/tex] is the final kinetic energy of the object
[tex]K_i[/tex] is the initial kinetic energy
Also, the work done on an object is (assuming that the force is applied parallel to the motion of the object):
[tex]W=F\Delta x[/tex]
where
F is the magnitude of the force
[tex]\Delta x[/tex] is the displacement of the object
In this problem, the force acting on the object is
F
While the displacement is the horizontal distance travelled, so
[tex]\Delta x = 3d[/tex]
Therefore, the work done is
[tex]W=(F)(3d)=3Fd[/tex]
And so the change in kinetic energy is
[tex]\Delta K = 3Fd[/tex]
Learn more about work and kinetic energy:
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