- #1
Chris2505
- 5
- 0
I'm trying to find the final velocity and the time taken for a particle to tavel a certain distance. I know the initial velocity and displacement and the force as a function of the velocity.
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 I am unsure about how to calculate the time taken for this displacement?
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 I am unsure about how to calculate the time taken for this displacement?