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I just finished class and my professor was writing some of Newton's Laws on the board and derived some equations. We ended up with:

V(Δt)=FΔt (this is for velocity in first inertial frame

V(2Δt)=2FΔt (this is for velocity in second inertial frame

Then he went and got the position in respect with time:V(2Δt)=2FΔt (this is for velocity in second inertial frame

x(Δt)=F(Δt)(Δt) (which is just the integral of velocity in first i.f.)

But then he did it for the second inertial frame and got:x(2Δt)=x(Δt)+2F(Δt)(Δt)

I do not understand where the x(Δt) comes from... Can anyone clarify this for me?