The equations of motion for free fall

Uniformly Accelerated Rectilinear Motion

In free fall, the acceleration is constant and equal to g (approximately 9.8 m/s²), directed downwards. The motion is therefore uniformly accelerated rectilinear motion (UARM).

The three equations of motion

We choose a vertical axis pointing downwards, with the origin at the starting point, where v₀ is the initial velocity (often zero if the object is simply dropped).

• Acceleration: a(t) = g
• Velocity: v(t) = g*t + v₀
• Position: y(t) = (1/2)gt² + v₀*t

Example: a ball dropped from a tower with no initial velocity (v₀ = 0). After t = 2 s: v = 9.8 * 2 = 19.6 m/s, and y = 0.5 * 9.8 * 2² = 19.6 m.

Summary table

Quantity	Formula	Unit
Acceleration	a = g	m/s²
Velocity	v(t) = g*t + v₀	m/s
Position	y(t) = (1/2)gt² + v₀*t	m

Pitfall to avoid

Do not confuse velocity (v, in m/s) with the distance travelled (y, in m): velocity increases linearly with time, whereas distance increases with the square of time. An object that falls for twice as long does not travel twice the distance, but four times the distance!