Free Fall & Gravitational Acceleration Cheat Sheet

A printable reference covering free fall, gravitational acceleration, kinematic equations, velocity, displacement, time, and sign conventions for grades 9-12.

TopicsPhysics Gravity Acceleration Motion Forces Time Study Guide

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Physics Vocabulary

Free fall describes the motion of an object when gravity is the only force causing its acceleration. This cheat sheet helps students organize the main equations, signs, and assumptions used in vertical motion problems. It is useful for solving dropped, thrown upward, and thrown downward object problems clearly and consistently. Near Earth's surface, gravitational acceleration is usually treated as constant with magnitude $g = 9.8\ \text{m/s}^2$ . The most important equations are the constant acceleration kinematics formulas, used with $a = -g$ if upward is chosen as positive. Direction matters, so velocity, displacement, and acceleration must be assigned signs before substituting values.

Key Facts

In ideal free fall, the only force acting on the object is gravity, so air resistance is ignored.
Near Earth's surface, gravitational acceleration has magnitude $g = 9.8\ \text{m/s}^2$ and points downward.
If upward is positive, the acceleration in free fall is $a = -g = -9.8\ \text{m/s}^2$ .
The velocity equation for free fall is $v = v_0 + at$ , where $a$ is usually $-g$ or $+g$ depending on the sign convention.
The displacement equation is $\Delta y = v_0 t + \frac{1}{2}at^2$ .
The velocity-displacement equation is $v^2 = v_0^2 + 2a\Delta y$ , which is useful when time is not given.
At the highest point of a vertical throw, the instantaneous velocity is $v = 0$ , but the acceleration is still $a = -g$ if upward is positive.
For motion that starts and ends at the same height, the time rising equals the time falling, and the launch speed equals the landing speed in magnitude.

Vocabulary

Free fall: Free fall is motion in which gravity is the only force affecting an object's acceleration.
Gravitational acceleration: Gravitational acceleration is the acceleration caused by gravity, with magnitude $g = 9.8\ \text{m/s}^2$ near Earth's surface.
Velocity: Velocity is speed with direction, so upward and downward motion must be represented with opposite signs.
Displacement: Displacement is the change in position, written as $\Delta y = y_f - y_i$ for vertical motion.
Initial velocity: Initial velocity, written $v_0$ , is the object's velocity at the start of the time interval being analyzed.
Sign convention: A sign convention is the choice of which direction is positive and which direction is negative in a motion problem.

Common Mistakes to Avoid

Using $g = 9.8\ \text{m/s}^2$ without a sign is incomplete because acceleration is a vector and must match the chosen positive direction.
Setting acceleration to zero at the top of the path is wrong because only the instantaneous velocity is $v = 0$ there, while gravity still acts downward.
Mixing upward-positive and downward-positive signs in the same problem gives inconsistent equations and often reverses the answer's direction.
Using distance instead of displacement can be wrong because $\Delta y$ depends on final position minus initial position, not total path length.
Assuming all falling objects in real life accelerate at exactly $g$ can be wrong because air resistance may be important for light, flat, or fast-moving objects.

Practice Questions

1 A ball is dropped from rest from a height of $45\ \text{m}$ . Ignoring air resistance, how long does it take to hit the ground if $g = 9.8\ \text{m/s}^2$ ?
2 A stone is thrown upward with initial velocity $v_0 = 20\ \text{m/s}$ . Using $a = -9.8\ \text{m/s}^2$ , what is its velocity after $1.5\ \text{s}$ ?
3 A rock is thrown downward from a cliff with $v_0 = 6\ \text{m/s}$ and lands after $3.0\ \text{s}$ . If downward is positive, what displacement does it travel using $\Delta y = v_0t + \frac{1}{2}gt^2$ ?
4 A ball is thrown straight upward and later returns to the same height. Explain why its acceleration does not become zero at the highest point.

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