Free Fall and Falling Objects Study Pack
Kibin's free study pack on Free Fall and Falling Objects includes a 6-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 27, 2026
Free Fall and Falling Objects Study Guide
Master the mechanics of free fall by working through gravitational acceleration, kinematic equations, and sign conventions for objects in vertical motion. Covers key concepts like peak-velocity zero, g = 9.8 m/s², and Galileo's mass-independence principle.
Key Takeaways
- •Free fall is motion under gravity alone, with no air resistance, producing a constant downward acceleration of approximately 9.8 m/s² near Earth's surface.
- •Because gravitational acceleration (g) is constant, the kinematic equations for uniform acceleration apply directly to free-fall problems.
- •An object in free fall gains speed at 9.8 m/s for every second it falls, meaning velocity increases linearly while displacement increases as the square of time.
- •At the peak of a vertically launched projectile's path, instantaneous velocity equals zero, but acceleration remains 9.8 m/s² downward throughout the entire flight.
- •The sign convention chosen for a problem (positive up or positive down) must be applied consistently to displacement, velocity, and acceleration to avoid calculation errors.
- •All objects in true free fall — regardless of mass — experience the same gravitational acceleration, a result confirmed by Galileo's experiments and explained by Newton's equivalence of gravitational and inertial mass.
Defining Free Fall and Gravitational Acceleration
Free fall describes a very specific physical situation: an object moving only under the influence of gravity, with no other forces — particularly no air resistance — acting on it. Understanding this definition precisely is the foundation for all free-fall calculations.
What Qualifies as Free Fall
- •An object is in free fall only when gravity is the sole force acting on it; a parachutist or feather falling through air is NOT in free fall because air resistance exerts an additional upward force.
- •In everyday problems at the introductory level, air resistance is typically ignored so that any dropped or thrown object can be treated as being in free fall.
- •Free fall applies to objects moving upward, downward, or momentarily at rest at a peak — the direction of motion does not change whether the object qualifies.
Gravitational Acceleration Near Earth's Surface
- •The acceleration due to gravity, symbolized g, has a standard value of 9.8 m/s² directed downward toward Earth's center.
- •This value holds approximately constant for objects near Earth's surface; it changes measurably only at very high altitudes or on other planets.
- •Because g is a constant acceleration, free fall is a specific case of uniformly accelerated motion, which means all kinematic equations for constant acceleration apply.
Galileo's Insight: Mass Independence
- •Galileo demonstrated — and Newton's law of gravitation later confirmed — that all objects in free fall accelerate at the same rate regardless of their mass.
- •A 1 kg ball and a 10 kg ball released simultaneously from the same height reach the ground at the same time (ignoring air resistance), because gravitational force scales with mass in exactly the same proportion as the inertia resisting that force.
Sign Conventions and Setting Up Free-Fall Problems
Before applying any equation to a free-fall problem, a consistent sign convention must be established for direction, because displacement, velocity, and acceleration are all vector quantities that can point either upward or downward.
Choosing a Coordinate System
- •The most common convention designates upward as positive (+) and downward as negative (−); under this convention, g is entered as −9.8 m/s² in equations.
- •An equally valid alternative takes downward as positive, in which case g = +9.8 m/s²; either choice produces the same physical result as long as it is applied consistently throughout the problem.
- •The chosen positive direction also determines the sign of initial velocity: an object thrown upward has a positive initial velocity under the upward-positive convention, while an object dropped from rest has an initial velocity of zero.
Identifying Known and Unknown Variables
- •Every free-fall problem involves some combination of five variables: displacement (Δy), initial velocity (v₀), final velocity (v), gravitational acceleration (g), and time (t).
- •Identifying which three variables are known determines which kinematic equation to apply, since each equation relates exactly four of these five quantities.
- •The phrase 'dropped from rest' signals v₀ = 0; 'at the highest point' signals v = 0 at that instant; 'returns to the same height' signals Δy = 0 for the full trip.
Kinematic Equations Applied to Vertical Motion
The four standard kinematic equations for constant acceleration translate directly to free-fall problems by substituting vertical displacement for position and using g for acceleration. Each equation is suited to a different set of known variables.
The Four Core Equations
- •v = v₀ + gt relates final velocity to initial velocity and elapsed time; useful when displacement is not needed.
- •Δy = v₀t + ½gt² relates displacement to initial velocity and time; the squared time term is what causes displacement to grow nonlinearly.
- •v² = v₀² + 2gΔy relates final velocity to initial velocity and displacement without requiring time; particularly efficient for problems where time is unknown.
- •Δy = ½(v₀ + v)t relates displacement to average velocity and time; useful as a quick check when both velocities are known.
How Velocity and Displacement Evolve During a Fall
- •Velocity increases linearly with time: every additional second of free fall adds 9.8 m/s to the object's speed in the downward direction.
- •Displacement increases as the square of time: an object falls 4.9 m in the first second, 19.6 m in the first two seconds, and 44.1 m in the first three seconds — each interval covers more distance than the last.
- •This nonlinear growth in displacement is the direct mathematical consequence of acceleration being constant rather than zero.
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Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.
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What is the standard value of gravitational acceleration near Earth's surface?
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Free Fall and Gravitational Acceleration
Explain what free fall means in your own words. What conditions must be true for an object to be considered in free fall, and what is the significance of the constant value g = 9.8 m/s²?
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