Acceleration is the rate of change of velocity over time. Formula: a = Δv/Δt. SI unit is m/s². Positive = speeding up; negative = slowing down (deceleration). Example: Car going 0 to 60 mph in 5 seconds has acceleration of 12 mph/s (5.37 m/s²).

1 g = 9.81 m/s², Earth's gravitational acceleration. When standing still, you experience 1 g downward. It's the reference point for comparing other accelerations. During free fall, 0 g (weightlessness). Fighter jets reach 6–9 g during maneuvers (feel 6–9 times heavier).

Average car 0-60 mph: ~0.5 g (5 m/s²). Sports car: 0.7–0.8 g (7–8 m/s²). Supercar: 1–1.2 g (10–12 m/s²). Formula 1: 1.5+ g (15+ m/s²). Tesla Model S Plaid: 1.1 g (10.8 m/s²). Higher g = faster acceleration, more thrilling feel.

m/s² is absolute acceleration (SI unit). g-force is relative to Earth's gravity (9.81 m/s²). 10 m/s² = 1.02 g. g-forces are intuitive for humans (pilots, riders), while m/s² is standard for physics/engineering. Both measure same thing, different scales.

G-forces relate acceleration to human experience. Humans understand gravity. Saying '6 g's' immediately means 'feel 6 times heavier' (58.9 m/s²). Pilots, astronauts, and drivers use g-forces for quick performance comparison. Physics/engineers use m/s² for precision calculations.

Automotive engineers (vehicle performance), aerospace engineers (pilot g-limits), physicists (motion analysis), mechanical engineers (impact testing), structural engineers (seismic analysis), amusement park designers (ride safety), smartphone engineers (accelerometer data), and sports scientists (athlete acceleration).

Centripetal acceleration = v² / r (velocity squared ÷ radius). It changes direction (not speed) toward center of circle. Example: Car turning 30 m/s on 50 m radius curve = 18 m/s² (1.8 g) centripetal acceleration. Used for cornering forces, roller coasters, planetary orbits.

Multiply ft/s² by 0.3048 to get m/s². Example: 32.2 ft/s² (Earth gravity) × 0.3048 = 9.81 m/s². Reverse: Divide m/s² by 0.3048 to get ft/s². 10 m/s² ÷ 0.3048 = 32.81 ft/s².

Free fall = object falling under gravity alone (no air resistance). Acceleration = 9.81 m/s² regardless of mass (proven by Galileo). Example: Drop ball and feather in vacuum—both reach ground simultaneously. Air resistance changes this in atmosphere, but physics value is constant 9.81 m/s².

Humans survive 3–4 g sustained (fighter pilots). 6–8 g for short periods (trained astronauts). 10–15 g for brief seconds (car crashes). Above 20 g = likely fatal. Tolerance depends on duration and direction (head-to-toe vs chest-to-back different). Professional training increases tolerance.

SpaceX Falcon 9: 3.8 g (37.3 m/s²) during first stage. Space Shuttle: 3 g (29.4 m/s²). Apollo Saturn V: 4 g (39.2 m/s²). Astronauts weigh 3–4 times more for 5–10 minutes during ascent. Modern rockets designed to minimize g-force stress on crew/equipment.

Smartphones contain MEMS accelerometers measuring acceleration in m/s² or g-force. Sensors detect 3 axes (x, y, z). Apps use data for step counting, fall detection, game motion control. Raw readings convert between m/s² and g-force for display. Example: Phone lying flat reads ~1 g downward from gravity.

Average acceleration = total Δv / total Δt (overall change). Instantaneous acceleration = change at exact moment in time (calculus derivative). Car accelerating 0–60 mph in 5 s: average 12 mph/s. But acceleration curve is uneven (faster at start, slower end). Instantaneous varies second-by-second.

For constant acceleration: a = 2 × Δx / Δt². Example: Object travels 50 meters in 5 seconds from rest. a = 2 × 50 / 5² = 100 / 25 = 4 m/s². Or use v = √(2 × a × x) to find velocity, then a = v / t.

F = m × a (Force = mass × acceleration). Double the force = double acceleration (mass constant). Double the mass = half acceleration (force constant). Example: 1000 kg car needing 5 m/s² requires 5,000 Newtons force. This converter solves 'a' part; mass/force data needed separately.

Crash tests measure deceleration (negative acceleration). 50 mph crash into wall = ~40 g deceleration (400+ m/s²) over 0.1 seconds. Airbags and seatbelts reduce peak g-force by spreading impact over time. Safety systems designed to keep occupant g-forces below 60–100 g to prevent injury.