Motion in Two and Three Dimensions (Physics)

Recall cards on kinematics in two and three dimensions: the position, displacement, and velocity vectors in unit-vector notation and their component forms; instantaneous velocity as the derivative of position and always tangent to the path; the acceleration vector as the first derivative of velocity and the second derivative of position; the independence of motion along perpendicular axes and the constant-acceleration equations applied per axis; projectile motion with zero horizontal acceleration and downward gravity, including the launch components, time of flight, maximum height, range, the 45-degree maximum, complementary launch angles, and the parabolic trajectory; uniform and nonuniform circular motion, centripetal acceleration expressed through speed, period, and angular frequency, and tangential and total acceleration; and relative motion, with the addition rules for position, velocity, and acceleration across reference frames and the invariance of acceleration between frames moving at constant relative velocity.