F = ma connects force, mass, and acceleration. Double the force, double the acceleration. Halve the mass, double the acceleration.

• 1 N = 1 kg·m/s²
• More force → more acceleration
• Less mass → more acceleration
• Vector quantity: has direction

Velocity is speed with direction. Acceleration is how fast velocity changes — speeding up, slowing down, or changing direction.

• Positive: speeding up
• Negative: slowing down (deceleration)
• Turning car: accelerating (direction changes)
• Constant speed ≠ zero acceleration if turning

G-force measures acceleration as multiples of Earth's gravity. 1g = 9.81 m/s². Fighter pilots feel 9g, astronauts 3-4g at launch.

• 1g = standing on Earth
• 0g = free fall / orbit
• Negative g = upward acceleration (blood to head)
• Sustained 5g+ requires training

International standard using m/s² as base with decimal scaling. CGS system uses Gal for geophysics.

• m/s² — SI base unit, universal
• km/h/s — automotive (0-100 km/h times)
• Gal (cm/s²) — geophysics, earthquakes
• milligal — gravity prospecting, tidal effects

US customary units still used in American automotive and aviation alongside metric standards.

• ft/s² — engineering standard
• mph/s — drag racing, car specs
• in/s² — small-scale acceleration
• mi/h² — rarely used (highway studies)

Aviation, aerospace, and medical contexts express acceleration as g-multiples for intuitive understanding of human tolerance.

• g-force — dimensionless ratio to Earth gravity
• Standard gravity — 9.80665 m/s² (exact)
• Milligravity — microgravity research
• Planetary g — Mars 0.38g, Jupiter 2.53g

Core equations relate acceleration, velocity, distance, and time under constant acceleration.

• v₀ = initial velocity
• v = final velocity
• a = acceleration
• t = time
• s = distance

Objects moving in circles accelerate toward center even at constant speed. Formula: a = v²/r

• Earth orbit: ~0.006 m/s² toward Sun
• Car turning: lateral g-force felt
• Roller coaster loop: up to 6g
• Satellites: constant centripetal acceleration

Near light speed, acceleration becomes complex. Particle accelerators achieve 10²⁰ g instantaneously at collision.

• LHC protons: 190 million g
• Time dilation affects perceived acceleration
• Mass increases with velocity
• Light speed: unreachable limit

Acceleration defines car performance. 0-60 mph time translates directly to average acceleration.

• Sports car: 0-60 in 3s = 8.9 m/s² ≈ 0.91g
• Economy car: 0-60 in 10s = 2.7 m/s²
• Tesla Plaid: 1.99s = 13.4 m/s² ≈ 1.37g
• Braking: -1.2g max (street), -6g (F1)

Aircraft design limits based on g-tolerance. Pilots train for high-g maneuvers.

• Commercial jet: ±2.5g limit
• Fighter jet: +9g / -3g capability
• Space Shuttle: 3g launch, 1.7g re-entry
• Eject at 14g (pilot survival limit)

Tiny acceleration changes reveal underground structures. Centrifuges separate substances using extreme acceleration.

• Gravity survey: ±50 microgal precision
• Earthquake: 0.1-1g typical, 2g+ extreme
• Blood centrifuge: 1,000-5,000g
• Ultracentrifuge: up to 1,000,000g

Multiply g-value by 10 for quick estimate (exact: 9.81)

• 3g ≈ 30 m/s² (exact: 29.43)
• 0.5g ≈ 5 m/s²
• Fighter at 9g = 88 m/s²

Divide 26.8 by seconds to 60mph

• 3 seconds → 26.8/3 = 8.9 m/s²
• 5 seconds → 5.4 m/s²
• 10 seconds → 2.7 m/s²

Divide by 2.237 to convert mph/s to m/s²

• 1 mph/s = 0.447 m/s²
• 10 mph/s = 4.47 m/s²
• 20 mph/s = 8.94 m/s² ≈ 0.91g

Divide by 3.6 (same as speed conversion)

• 36 km/h/s = 10 m/s²
• 100 km/h/s = 27.8 m/s²
• Quick: divide by ~4

1 Gal = 0.01 m/s² (centimeters to meters)

• 100 Gal = 1 m/s²
• 1000 Gal ≈ 1g
• 1 milligal = 0.00001 m/s²

Mars ≈ 0.4g, Moon ≈ 0.17g, Jupiter ≈ 2.5g

• Mars: 3.7 m/s²
• Moon: 1.6 m/s²
• Jupiter: 25 m/s²
• Venus ≈ Earth ≈ 0.9g

Tesla Plaid: 0-60 mph in 1.99s. What's the acceleration?

60 mph = 26.82 m/s. a = Δv/Δt = 26.82/1.99 = 13.5 m/s² = 1.37g

F-16 pulling 9g in ft/s²? Earthquake at 250 Gal in m/s²?

Jet: 9 × 9.81 = 88.3 m/s² = 290 ft/s². Earthquake: 250 × 0.01 = 2.5 m/s²

Jump with 3 m/s velocity on Moon (1.62 m/s²). How high?

v² = v₀² - 2as → 0 = 9 - 2(1.62)h → h = 9/3.24 = 2.78m (~9 ft)

A flea accelerates at 100g when jumping — faster than a space shuttle launch. Their legs act like springs, releasing energy in milliseconds.

Accelerates its club at 10,000g, creating cavitation bubbles that collapse with light and heat. Aquarium glass doesn't stand a chance.

Human brain can survive 100g for 10ms, but only 50g for 50ms. American football hits: 60-100g regularly. Helmets spread impact time.

Large Hadron Collider accelerates protons to 99.9999991% light speed. They experience 190 million g, circling the 27km ring 11,000 times per second.

Earth's gravity varies by ±0.5% due to altitude, latitude, and underground density. Hudson Bay has 0.005% less gravity due to ice age rebound.

US Air Force sled hit 1,017g deceleration in 0.65s using water brakes. Test dummy survived (barely). Human limit: ~45g with proper restraints.

Felix Baumgartner's 2012 jump from 39km hit 1.25 Mach in free fall. Acceleration peaked at 3.6g, deceleration at parachute opening: 8g.

Atomic gravimeters detect 10⁻¹⁰ m/s² (0.01 microgal). Can measure height changes of 1cm or underground caves from surface.

Aristotle claimed heavier objects fall faster. Galileo proved him wrong by rolling bronze balls down inclined planes (1590s). By diluting gravity's effect, Galileo could time acceleration with water clocks, discovering that all objects accelerate equally regardless of mass.

Newton's Principia (1687) unified the concept: F = ma. Force causes acceleration inversely proportional to mass. This single equation explained falling apples, orbiting moons, and cannon trajectories. Acceleration became the link between force and motion.

• 1590: Galileo's inclined plane experiments measure constant acceleration
• 1638: Galileo publishes Two New Sciences, formalizing kinematics
• 1687: Newton's F = ma connects force, mass, and acceleration
• Established g ≈ 9.8 m/s² through pendulum experiments

19th-century scientists used reversible pendulums to measure local gravity to 0.01% precision, revealing Earth's shape and density variations. The Gal unit (1 cm/s², named for Galileo) was formalized in 1901 for geophysical surveys.

In 1954, the international community adopted 9.80665 m/s² as standard gravity (1g)—chosen as sea level at 45° latitude. This value became the reference for aviation limits, g-force calculations, and engineering standards worldwide.

• 1817: Kater's reversible pendulum achieves ±0.01% gravity precision
• 1901: Gal unit (cm/s²) standardized for geophysics
• 1940s: LaCoste gravimeter enables 0.01 milligal field surveys
• 1954: ISO adopts 9.80665 m/s² as standard gravity (1g)

WWII fighter pilots experienced blackouts during tight turns—blood pooled away from the brain under sustained 5-7g. Post-war, Col. John Stapp rode rocket sleds to test human tolerance, surviving 46.2g in 1954 (deceleration from 632 mph to zero in 1.4 seconds).

The Space Race (1960s) required understanding sustained high-g. Yuri Gagarin (1961) endured 8g launch and 10g re-entry. Apollo astronauts faced 4g. These experiments established: humans tolerate 5g indefinitely, 9g briefly (with g-suits), but 15g+ risks injury.

• 1946-1958: John Stapp rocket sled tests (46.2g survival)
• 1954: Ejection seat standards set at 12-14g for 0.1 seconds
• 1961: Gagarin's flight proves human space travel viable (8-10g)
• 1960s: Anti-g suits developed allowing 9g fighter maneuvers

The Large Hadron Collider (2009) accelerates protons to 99.9999991% light speed, achieving 1.9×10²⁰ m/s² (190 million g) in circular acceleration. At these speeds, relativistic effects dominate—mass increases, time dilates, and acceleration becomes asymptotic.

Meanwhile, atomic interferometer gravimeters (2000s+) detect 10 nanogal (10⁻¹¹ m/s²)—so sensitive they measure 1cm height changes or underground water flow. Applications range from oil prospecting to earthquake prediction and volcano monitoring.

• 2000s: Atomic gravimeters achieve 10 nanogal sensitivity
• 2009: LHC begins operation (protons at 190 million g)
• 2012: Gravity mapping satellites measure Earth's field to microgal precision
• 2020s: Quantum sensors detect gravitational waves via tiny accelerations