Free Fall

Acceleration is the rate velocity changes, not the velocity itself. A ball thrown straight up slows down, stops for an instant, then speeds up downward. At that top instant, velocity is zero, but gravity never switched off. The acceleration stays a constant 9.8 m/s² downward the whole flight, before, during, and after the turnaround. That constant acceleration is exactly what makes the turnaround happen: it steadily eats away at the upward velocity until none is left, then keeps pushing the ball into negative (downward) velocity.

Because acceleration is constant, the same three kinematics equations from straight-line motion apply directly, with a = -g if up is positive. At maximum height v = 0, so v0² = 2 g h solves for height. For time of flight, the motion is symmetric: time up equals time down, so total time is 2 v0 / g. This symmetry exists because the acceleration is constant and the same going up and coming down, so the upward and downward trips mirror each other in speed at every height.

Free fall is the cleanest example of constant acceleration kinematics, setting up everything else in this unit. The same position-velocity-acceleration relationships, now understood as derivatives and integrals of each other, carry over once motion gains a horizontal component in projectile motion, where vertical free fall and constant horizontal velocity happen independently along perpendicular axes.