I've been trying to obtain an equation of position in terms of time given force in terms of position. I've tried and I think I've managed to obtain an equation of velocity in terms of position using work and kinetic energy but I haven't managed the position time equation.(adsbygoogle = window.adsbygoogle || []).push({});

This is how I got velocity equation:

A point mass [itex]m[/itex] is at starting position [itex]x=0[/itex] with starting velocity [itex]v_0[/itex]

[itex]F=x+1[/itex]

[itex]W=\int_0^x {(x+1)dx}=\frac{x^2+2x}2[/itex]

[itex]\frac 1 2 m(v^2-{v_0}^2)=\frac{x^2+2x}2[/itex]

[itex]v=\sqrt{\frac{x^2+2x}m+{v_0}^2}[/itex]

How do I get a position-time equation? And how do I use a starting position other than x = 0?

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# Position-time equation from force-position equation

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