# Position-time equation from force-position equation

by Droctagonopus
Tags: equation, forceposition, positiontime
 P: 28 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. This is how I got velocity equation: A point mass $m$ is at starting position $x=0$ with starting velocity $v_0$ $F=x+1$ $W=\int_0^x {(x+1)dx}=\frac{x^2+2x}2$ $\frac 1 2 m(v^2-{v_0}^2)=\frac{x^2+2x}2$ $v=\sqrt{\frac{x^2+2x}m+{v_0}^2}$ How do I get a position-time equation? And how do I use a starting position other than x = 0?