I am currently coding something with a moving object and can't figure out the physics with my school knowledge only. I hope this question is not below the standards of this forum.
I have a moving object at ($x_0, y_0, \theta_0, v_0, \omega_0$), where $x$ and $y$ are the 2D-coordinates, $\theta$ the angle (to the x axis), $v$ the forward velocity and $\omega$ the angular velocity.
I want to accelerate the object with a forward acceleration of $a$ and an angular acceleration of $\alpha$ and I want to calculate the new position after a time $\Delta t$.
If $\alpha = 0$ (just as an intermediate step), the new state should be $$ x_1 = x_0 + \Delta t (v_0 \cos \theta_0) + 0.5 a (\Delta t^2) \\ y_1 = y_0 + \Delta t (v_0 \sin \theta_0) + 0.5 a (\Delta t^2) \\ \theta_1 = \theta_0 + \omega_0 \Delta t \\ v_1 = v_0 + a \Delta t \\ \omega_1 = \omega_0 $$ I am not sure if this is correct, but this is all I have. And I can't figure out how to add the angular acceleration to this equations, and I guess $\omega$ should be in the equations for $x$ and $y$ too.