Acceleration

Acceleration acceleration Acceleration  is a vector quantity that is defined as the rate at which an object changes its velocity...

• Acceleration
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acceleration

• Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

• Any change in the velocity of an object results in an acceleration: increasing speed (what people usually mean when they say acceleration), decreasing speed (also called deceleration or retardation), or changing direction. Yes, that's right, a change in the direction of motion results in an acceleration even if the moving object neither sped up nor slowed down. That's because acceleration depends on the change in velocity and velocity is a vector quantity — one with both magnitude and direction. Thus, a falling apple accelerates, a car stopping at a traffic light accelerates, and an orbiting planet accelerates. Acceleration occurs anytime an object's speed increases or decreases, or it changes direction.

Average acceleration

An object's average acceleration over a period of time is its change in velocity  divided by the duration of the period . Mathematically,

• ${\displaystyle \mathbf {\bar {a}} ={\frac {\Delta \mathbf {v} }{\Delta t}}.}$

  Instantaneous acceleration

  Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time.

  instantaneous acceleration is measured over a "short" time interval. The word short in this context means infinitely small or infinitesimal — having no duration or extent whatsoever. It's a mathematical ideal that can can only be realized as a limit. The limit of a rate as the denominator approaches zero is called a derivative. Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero — or alternatively, acceleration is the derivative of velocity.

  a =	lim	Δv	=	dv
  	Δt→0	Δt		dt

  Units

  Calculating acceleration involves dividing velocity by time — or in terms of units, dividing meters per second [m/s] by second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus the SI unit of acceleration is the meter per second squared.

  ⎡ ⎣	m	=	m/s	=	m		1	⎤ ⎦
  	s2		s		s		s

  Another frequently used unit is the acceleration due to gravity — g.

  Here are some sample accelerations to end this section.

  Acceleration of selected events (smallest to largest)

  a (m/s2)	event
  5 × 10−14	smallest acceleration in a scientific experiment
  2 × 10−10	galactic acceleration at the sun
  9 × 10−10	anomalous acceleration of pioneer spacecraft
  0.5	elevator, hydraulic
  0.63	free fall acceleration on Pluto
  1	elevator, cable
  1.6	free fall acceleration on the moon
  8.8	International Space Station
  3.7	free fall acceleration on mars
  9.8	free fall acceleration on earth
  10–40	manned rocket at launch
  20	space shuttle, peak
  24.8	free fall acceleration on Jupiter
  20–50	roller coaster
  80	limit of sustained human tolerance
  0–150	human training centrifuge
  100–200	ejection seat
  270	free fall acceleration on the sun
  600	airbags automatically deploy
  104–106	medical centrifuge
  106	bullet in the barrel of a gun
  106	free fall acceleration on a white dwarf star
  1012	free fall acceleration on a neutron star

  Automotive accelerations (g)

  event	typical car	sports car	F-1 race car	large truck
  starting	0.3–0.5	0.5–0.9	1.7	< 0.2
  braking	0.8–1.0	1.0–1.3	2	~ 0.6
  cornering	0.7–0.9	0.9–1.0	3	?

  Acceleration and the human body

  a (g)	event
  2.9	sneeze
  3.5	cough
  3.6	crowd jostle
  4.1	slap on back
  8.1	hop off step
  10.1	plop down in chair
  60	chest acceleration during car crash at 48 km/h with airbag
  70–100	crash that killed Diana, Princess of Wales, 1997
  150–200	head acceleration limit during bicycle crash with helmet