The only force acting on a 2.0kg body as it moves along a positive x-axis has an x-component Fx=-6x with x in meters.The velocity at x =3.0m is 8.0m/s.The velocity of the body at x=4.0m is?
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equation for the force is given as
= - 6x
= initial position = 3 m
= final position = 4 m
work done by a force is given as
W = dx
W = (- 6x) dx
W = - 3 ((4²) - (3)²)
W = - 21 J
m = mass of the body = 2 kg
v₁ = initial velocity = 8 m/s
v₂ = final velocity = ?
Using work-change in kinetic energy theorem
Work done = change in kinetic energy
Work done = final Kinetic energy - initial kinetic energy
W = (0.5) m (v²₂ - v²₁)
- 21 = (0.5) (2) (v²₂ - 8²)
v₂ = 6.6 m/s
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