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A 6 kg rock is subject to a variable force given by the equation F(x) =...

A 6 kg rock is subject to a variable force given by the equation F(x) = 6 + 2x. IF the rock is initially at rest at the origin. find its speed when it has moved 9 m.

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Answer #1

Initial kinetic energy is zero.

Final kinetic energy is

Where v is the speed of the rock at x=9m.

Workdone by Force F(x) in moving the rock to a distance of 9 metres is

Since Force and displacement are in same direction therefore =0.

Therefore,

By work-energy theorem

Hence, speed of the rock at when it has moved 9m is

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