In a two-dimensional environment: Given: a starting point (x1,y1) an initial velocity (speed and 2D heading/direction) a constant rate of turning (yaw, since there is no roll or pitch in only two dimensions) a constant acceleration of the object from itself (not like gravity where the direction of the acceleration is relatively constant - "down" - but like a rocket that is propelling itself) a time change t1 to t2 What is the formula for the final point (x2,y2)? What kind of physics problem do I have on my hands? Is this just a variation on kinematics with variable acceleration (varying direction of acceleration instead of amount), or is it qualitatively different? There is no sliding. (turning without accelerating example) If it is headed north/up from (0,0) and turns 90 degrees to the right at a speed of pi/10 per second, then after 10 seconds it will be at (2,2). I just guessed at thread title prefix thread level. Let me know if it is incorrect and I can try to change it.