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Using: [itex]F = ma[/itex] so [itex]\frac{F(v)}{m} = v \frac{dv}{ds}[/itex]

so: [itex]\int ds = m \int v \frac{dv}{F(v)}[/itex]

Rearanging and using limts gives final velocity as a function of dispacement and initial velocity. However im unsure about how to calculate the time taken for this displacement?