What is the formula to calculate vertical acceleration? How is it different from general acceleration?

Vertical acceleration follows the same fundamental formula a = (v - u) / t or a = dv/dt as any acceleration, but in most Earth-based scenarios it equals or includes gravitational acceleration g = 9.8 m/s² downward. For free-falling objects with no air resistance, vertical acceleration is constant at 9.8 m/s² regardless of the object's velocity or mass—this is the defining characteristic of gravitational acceleration. A feather and hammer dropped simultaneously in a vacuum fall with identical acceleration, though on Earth, air resistance modifies the feather's acceleration significantly.

The difference from general acceleration is contextual rather than mathematical: vertical problems typically involve gravity as a constant component, while horizontal problems don't. For a projectile launched upward, vertical acceleration is -9.8 m/s² (taking upward as positive) throughout the entire flight, causing the upward velocity to decrease, reach zero at peak height, then become increasingly negative (downward) during descent. Calculating vertical displacement uses s_y = u_y·t + ½a_y·t² with a_y = -9.8 m/s², while horizontal motion has a_x = 0 (no horizontal acceleration in ideal projectile motion).

When air resistance becomes significant, vertical acceleration is no longer constant but depends on velocity through drag force: a = g - (b·v²/m), where b is a drag coefficient. Skydivers experience decreasing downward acceleration as they speed up, eventually reaching terminal velocity when drag force equals weight and acceleration becomes zero. For powered vertical motion like rockets or elevators, net vertical acceleration is a = (F_thrust - mg) / m, combining engine force with gravitational force. Rocket launches require thrust acceleration exceeding 9.8 m/s² just to overcome gravity and achieve upward motion—this is why launch accelerations typically range from 3-4 g initially.