This is a simulation of the motion of a ball that has a rocket engine mounted underneath it. The ball is released from rest from a height of 40 meters above the ground, and it falls 20 meters under the influence of gravity alone. At that point, the rocket engine kicks in, giving the ball an upward acceleration of 10 m/s/s (as opposed to the acceleration downward of 10 m/s/s that it just had).

You can see the ball's motion diagram as well as graphs of the ball's position, velocity, and acceleration, all as a function of time.