How do you find the displacement of an object if you know the acceleration?

Dec 6, 2016

If the displacement is $x$, then;

velocity is $v = \frac{\mathrm{dx}}{\mathrm{dt}}$

Acceleration is $a = \frac{\mathrm{dv}}{\mathrm{dt}} = \frac{{d}^{2} x}{\mathrm{dt}} ^ 2$

So if you know the acceleration then the displacement is found by solving the differential equation:

$\frac{{d}^{2} x}{\mathrm{dt}} ^ 2 = a \left(t\right)$