Describe free fall as motion under the constant acceleration due to gravity, and apply the kinematic equations with $g = 9.81$ m/s squared to objects dropped, thrown down or thrown up near Earth's surface.

What this topic is asking

Free fall is the simplest application of the kinematic equations: motion under gravity alone. The Physical Setting/Physics course asks you to recognize that, with air resistance neglected, every object near Earth's surface accelerates downward at the same rate, $g = 9.81$ m/s squared, and to use the kinematic equations to find times, speeds and heights for dropped and thrown objects. The Regents tests this in quick concept items and in constructed-response calculations.

The acceleration due to gravity

A heavy object and a light object dropped together hit the ground at the same instant in free fall, because gravity gives them the same acceleration, not the same force. This surprises many students, who expect the heavier object to fall faster; the heavier object does feel a larger force (its weight), but it also has more mass to accelerate, and the two effects cancel exactly. Air resistance, which the Regents usually tells you to neglect, is what makes a feather fall slower than a coin in everyday life.

Applying the kinematic equations to free fall

Because the acceleration is constant, free fall is just the constant-acceleration kinematics of the kinematic equations with $a = g$. Choose downward (or upward) as positive and stick to it. Three standard cases appear:

• Dropped from rest: $v_i = 0$, so $d = \tfrac{1}{2}gt^2$ and $v_f = gt$.
• Thrown downward: $v_i$ is the launch speed downward, and gravity adds to it.
• Thrown upward: the object decelerates on the way up, stops momentarily at the top where $v = 0$, then speeds up on the way down. The acceleration is $g$ downward the whole time, including at the highest point.

The turning point of an object thrown up

This symmetry is a favorite Regents idea. The common error is to think the acceleration is zero at the top because the velocity is zero; in fact gravity acts continuously, which is exactly why the object does not hang there but immediately falls.

Reference Tables note

The value $g = 9.81$ m/s squared appears in the List of Physical Constants on the Reference Tables, so use it (not $10$) unless told otherwise. There is no separate "free fall" equation; you use the standard kinematic equations with $a = g$. The weight of a falling object, $F_g = mg$, is also printed and links free fall to forces, but in pure kinematics you work with the acceleration $g$ directly.

Try this

Q1. State the acceleration of a freely falling object, including its direction, and say whether it depends on mass. [2 points]

• Cue. $9.81$ m/s squared downward; it does not depend on mass.

Q2. An object is dropped from rest. Calculate its speed after $1.5$ s ($g = 9.81$ m/s squared). [2 points]

• Cue. $v_f = gt = (9.81)(1.5) = 14.7$ m/s, about $15$ m/s.