Motion in Two Dimensions with Constant Acceleration
A particle starting at position with initial velocity subjected to a constant acceleration follows a trajectory given by . For one-dimensional motion, say in the direction, this reduces to . A projectile fired upward at an angle describes a parabolic trajectory when subject to the downward acceleration of gravity. The path of the particle up to the time is shown by a dotted curve.
Snapshot 1: linear motion when the velocity and acceleration are in the same direction
Snapshot 2: parabolic trajectory of a missile
Snapshot 3: a weight dropped, possibly off the Tower of Pisa, with a slight forward push
You can animate these simulations with the animation button on the time slider. Use the slow motion option.
Reference: E. Kasner, "The Trajectories of Dynamics," Transactions of the American Mathematical Society, 7(3) 1906 pp. 401–424.