Numerical integration: Acceleration → Velocity → Position

If data for acceleration is available in tabular form, this page can be used to numerically integrate the acceleration to obtain the velocity and the position. Paste the data for a component of the acceleration vector into the red box and press the 'calculate from table' button. Simpson's rule is used to integrate the data to determine the velocity and the postion.

It is also possible to fill the red textbox with data by typing a formula into the blue textbox and pressing the "Calculate from formula" button. This formula is used to fill the table with 1000 equally spaced values of $a_x(t)$ equally spaced between $t_1$ and $t_2$.

$a_x(t)=$  [m/s²]
in the range from $t_1=$  [s] to $t_2=$  [s].

 $t$   $a_x(t)$

  

$a_x(t)$

$t$

The velocity is the integral of the acceleration,

$\large v_x(t)=\int\limits_{t_1}^{t} a_x(t')dt' +v_x(t_1)$.

Here $v_x(t_1)$ is the integration constant.

$v_x(t_1)=$

 $t$   $v_x(t)$

  

$v_x(t)$

$t$

The position is the integral of the velocity.

$\large r_x(t) = \int \limits_{t_1}^{t} v_x(t')dt' + r_x(t_1).$

Where $r_x(t_1)$ is the integration constant.

$x(t_1)=$

 $t$   $x(t)$

  

$x(t)$

$t$

Questions