Acceleration – The Physics Hypertextbook (2022)

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When the velocity of an object changes it is said to be accelerating. Acceleration is the rate of change of velocity with time.

In everyday English, the word acceleration is often used to describe a state of increasing speed. For many Americans, their only experience with acceleration comes from car ads. When a commercial shouts "zero to sixty in six point seven seconds" what they're saying here is that this particular car takes 6.7s to reach a speed of 60mph starting from a complete stop. This example illustrates acceleration as it is commonly understood, but acceleration in physics is much more than just increasing speed.

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 (called centripetal acceleration). 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 the moon in orbit around the Earth accelerates. Acceleration occurs anytime an object's speed increases or decreases, or it changes direction.

Much like velocity, there are two kinds of acceleration: average and instantaneous. Average acceleration is determined over a "long" time interval. The word long in this context means finite — something with a beginning and an end. The velocity at the beginning of this interval is called the initial velocity, represented by the symbol v0 (veenought), and the velocity at the end is called the final velocity, represented by the symbol v (vee). Average acceleration is a quantity calculated from two velocity measurements.

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In contrast, 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 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.


Acceleration is the derivative of velocity with time, but velocity is itself the derivative of position with time. The derivative is a mathematical operation that can be applied multiple times to a pair of changing quantities. Doing it once gives you a first derivative. Doing it twice (the derivative of a derivative) gives you a second derivative. That makes acceleration the first derivative of velocity with time and the second derivative of position with time.


A word about notation. In formal mathematical writing, vectors are written in boldface. Scalars and the magnitudes of vectors are written in italics. Numbers, measurements, and units are written in roman (not italic, not bold, not oblique — ordinary text). For example…


(Design note: I think Greek letters don't look good on the screen when italicized so I have decided to ignore this rule for Greek letters until good looking Greek fonts are the norm on the web.)

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international units

Calculating acceleration involves dividing velocity by time — or in terms of SI units, dividing the meter per second [m/s] by the 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.



natural units

Another frequently used unit is the standard acceleration due to gravity — g. Since we are all familiar with the effects of gravity on ourselves and the objects around us it makes for a convenient standard for comparing accelerations. Everything feels normal at 1g, twice as heavy at 2g, and weightless at 0g. This unit has a precisely defined value of9.80665m/s2, but for everyday use 9.8m/s2 is sufficient, and 10m/s2 is convenient for quick estimates.

The unit called the standard acceleration due to gravity (represented by a roman g) is not the same as the natural phenomenon called acceleration due to gravity (represented by an italic g). The former has a defined value whereas the latter has to be measured. (More on this later.)

Although the term "gforce" is often used, the g is a measure of acceleration, not force. (More on forces later.) Of particular concern to humans are the physiological effects of acceleration. To put things in perspective, all values are stated in g.

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  • In roller coaster design, speed is of the essence. Or, is it? If speed was all there was to designing a thrill ride, then the freeway would be pretty exciting. Most roller coaster rarely exceed 30m/s (60mph). Contrary to popular belief, it is the acceleration that makes the ride interesting. A well designed roller coaster will subject the rider to maximum accelerations of 3 to 4g for brief periods. This is what gives the ride its dangerous feel.
  • Despite the immense power of its engines, the acceleration of the Space Shuttle was kept below 3g. Anything greater would put unnecessary stress on the astronauts, the payload, and the ship itself. Once in orbit, the whole system enters into an extended period of free fall, which provides the sensation of weightlessness. Such a "zerog" environment can also be simulated inside a specially piloted aircraft or a free fall drop tower. (More on this later.)
  • Fighter pilots can experience accelerations of up to 8g for brief periods during tactical maneuvers. If sustained for more than a few seconds, 4 to 6g is sufficient to induce blackout. To prevent "g-force loss of consciousness" (G-LOC), fighter pilots wear special pressure suits that squeeze the legs and abdomen, forcing blood to remain in the head.
  • Pilots and astronauts may also train in human centrifuges capable of up to 15g. Exposure to such intense accelerations is kept brief for safety reasons. Humans are rarely subjected to anything higher than 8g for longer than a few seconds.
  • Acceleration is related to injury. This is why the most common sensor in a crash test dummy is the accelerometer. Extreme acceleration can lead to death. The acceleration during the crash that killed Diana, Princess of Wales, in 1997 was estimated to have been on the order of 70 to 100g, which was intense enough to tear the pulmonary artery from her heart — an injury that is nearly impossible to survive. Had she been wearing a seat belt, the acceleration would have been something more like 30 or 35g — enough to break a rib or two, but not nearly enough to kill most people.

Gaussian units

The precise measurement of the strength of gravity over the surface of the Earth or other celestial objects is called gravimetry. For historical reasons the preferred unit in this field is the centimeter per second squared also known as the gal. In symbolic form…


Yes, that's right. The name of the unit is written all in lowercase (gal) while the symbol is capitalized (Gal). The gal was named in honor of the Italian scientist Galileo Galilei (1564–1642) who was the first scientist to study the acceleration due to gravity — and maybe was the first scientist of any sort. Since the acceleration due to gravity varies by only small amounts over the surface of most celestial objects, deviations in strength from idealized models (called gravitational anomalies) are measured in thousandths of a gal or milligals (mGal).


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The gal and milligal are part of a precursor to the International System of Units called the centimeter-gram-second system or Gaussian system of units. I may one day actually write something significant in that section of this book.

Here are some sample accelerations to end this section.

Acceleration of selected events (smallesttolargest)
a (m/s2)device, event, phenomenon, process
0stationary or moving at a constant velocity
5×10−14smallest acceleration in a scientific experiment
2.32×10−10galactic acceleration at the Sun
9×10−10anomalous acceleration of Pioneer spacecraft
0.5elevator, hydraulic
0.63free fall acceleration on Pluto
1elevator, cable
1.6free fall acceleration on the moon
8.8International Space Station in orbit
3.7free fall acceleration on Mars
9.8free fall acceleration on Earth
10–40manned rocket at launch
20space shuttle, peak
24.8free fall acceleration on Jupiter
20–50roller coaster
80limit of sustained human tolerance
0–150human training centrifuge
100–200ejection seat
270free fall acceleration on the Sun
600airbags automatically deploy
104–106medical centrifuge
106bullet in the barrel of a gun
106free fall acceleration on a white dwarf star
1012free fall acceleration on a neutron star
Automotive accelerations (g)
eventtypical carsports carF-1 race carlarge truck
Acceleration and the human bodyPrimary source:Acceleration perturbations of daily living, 1994
a (g)event
03.6crowd jostle
04.1slap on back
08.1hop off step
10.1plop down in chair
60chest acceleration during car crash at 48 km/h with airbag
70–100crash that killed Diana, Princess of Wales, 1997
150–200head acceleration limit during bicycle crash with helmet


How do you solve for acceleration in physics? ›

The equation for calculating acceleration is:
  1. Acceleration = (change in velocity)/(change in time) or. a = Δv ÷ Δt.
  2. Force = mass * acceleration. or. F = ma.
  3. acceleration = force/mass. or. a = F/m.

What is acceleration 7th grade? ›

Acceleration is defined as. The rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.

What is the unit of acceleration in physics? ›

Therefore, the SI unit of acceleration is the meter per second squared or (ms2).

What is velocity Science Grade 7? ›

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance.

What are 4 examples of acceleration? ›

  • An object was moving north at 10 meters per second. ...
  • An apple is falling down. ...
  • Jane is walking east at 3 kilometers per hour. ...
  • Tom was walking east at 3 kilometers per hour. ...
  • Sally was walking east at 3 kilometers per hour. ...
  • Acceleration due to gravity.

What are the 3 formulas for acceleration? ›

Acceleration formula – three acceleration equations
  • a = (v_f - v_i) / Δt ;
  • a = 2 × (Δd - v_i × Δt) / Δt² ;
  • a = F / m ;
6 Oct 2022

Is acceleration can be zero? ›

Derivative of velocity with respect to time is acceleration. That means if accelerations is zero, velocity must be constant. Now that constant could be anything like it could be 5 m/s . Also if the velocity is 0(which is itself a constant) also indicates that acceleration is zero.

How acceleration is defined? ›

acceleration, rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant, because the direction is continually changing.

Is an example of acceleration? ›

If an object is speeding up and moving in a positive direction, it has a positive acceleration. The car speeding up in the first example was an example of positive acceleration. The car is moving forward in a positive direction and speeding up, so the acceleration is in the same direction as the cars motion.

What is the symbol for acceleration? ›

In physics or physical science, acceleration (symbol: a) is defined as the rate of change (or derivative with respect to time) of velocity.

What is acceleration velocity? ›

Acceleration. Velocity is the rate of change of displacement. Acceleration is the rate of change of velocity. Velocity is a vector quantity because it consists of both magnitude and direction. Acceleration is also a vector quantity as it is just the rate of change of velocity.

What causes acceleration? ›

A net force on an object changes its motion – the greater the net force, the greater the acceleration. More massive objects require bigger net forces to accelerate the same amount as less massive objects.

What are the 3 types of velocity? ›

Types of Velocity
  • Uniform Velocity.
  • Variable Velocity.
  • Average Velocity.
  • Instantaneous Velocity.
30 Sept 2022

Is velocity a speed? ›

Why is it incorrect to use the terms speed and velocity interchangeably? The reason is simple. Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

What are 5 examples of velocity? ›

The applications of velocity are illustrated by the examples below:
  • Earth's rotation around the Sun,
  • Moon's orbital motion around the Earth.
  • The vehicle's speed.
  • How quickly the train is moving.
  • The river is moving at a fluctuating speed.
  • The rate at which water leaves a faucet.
  • The speed at which a bat strikes a ball.

What 3 things affect acceleration? ›

3 Factors Affecting Business Acceleration
  • The growth of your product can be linked to three factors: energy, friction, and direction.
  • Energy is required to get something in motion. ...
  • The goal is to apply an appropriate amount of energy to achieve a business objective.
  • Friction is the resistance that prevents acceleration.

What are the two types of acceleration? ›

Acceleration occurs anytime an object's speed increases or decreases, or it changes direction. Much like velocity, there are two kinds of acceleration: average and instantaneous.

What is the acceleration of all objects? ›

When gravity pulls objects toward the ground, it always causes them to accelerate at a rate of 9.8 m/s2. Regardless of differences in mass, all objects accelerate at the same rate due to gravity unless air resistance affects one more than another.

How do u calculate velocity? ›

Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt.

What is s in acceleration formula? ›

The S.I unit for acceleration is meter per second square or m/s2.

Why is acceleration m s2? ›

Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are m/s2, meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.

Can an acceleration be negative? ›

If you always choose the current direction of motion as positive, then an object that is slowing down will always have a negative acceleration.

What is 0 acceleration called? ›

So your acceleration is zero, then call it constant acceleration. Your velocity is zero, then call it constant velocity. And your displacement is zero, then you should be able to call it constant displacement (because your displacement doesn't change with the time in this case).

What is zero acceleration called? ›

If the change in velocity is zero i.e. either the object is at rest or moving with uniform velocity then the object is said to have zero acceleration.Example: a parked car a train moving with a constant speed of 90 km/hr.

What is acceleration and its types? ›

Acceleration occurs anytime an object's speed increases or decreases, or it changes direction. Much like velocity, there are two kinds of acceleration: average and instantaneous. Average acceleration is determined over a "long" time interval.

What is law of acceleration simple? ›

The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting upon an object is increased, the acceleration of the object is increased.

How does acceleration affect speed? ›

If the speed is increasing, the car has positive acceleration. When the car slows down, the speed decreases. The decreasing speed is called negative acceleration. In both cases, the car is accelerating, but one acceleration is positive and one is negative.

What does 2 mean in acceleration? ›

Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are m/s2, meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.

Is acceleration a vector? ›

Velocity and acceleration are vector quantities, so they have both magnitude and direction.

Is acceleration due to gravity? ›

We represent acceleration due to gravity by the symbol g. Its standard value on the surface of the earth at sea level is 9.8 ms². Its computation formula is based on Newton's Second Law of Motion and Newton's Law of Universal Gravitation.

Is acceleration high speed? ›

While acceleration and maximum speed are two different qualities, acceleration is the process by which an athlete attempts to move toward maximum speed. For this reason, the process of acceleration goes through distinct phases.

What is average acceleration formula? ›

Similarly, the average acceleration is the final velocity minus the initial velocity per time is taken. Therefore, the formula for average acceleration formula is: Aavg = Δv / Δt.

Is acceleration the same as speed? ›

While speed is distance covered in a unit of time, acceleration is the rate of change of speed that also takes into consideration direction.

Is acceleration a force? ›

Force is a push or pull that an object can exert on other objects. Acceleration is the rate of change of an object's speed. If an object has mass, and is accelerating through space, then the object can exert a force.

Is acceleration a force mass? ›

Force (N) = mass (kg) × acceleration (m/s²). Thus, an object of constant mass accelerates in proportion to the force applied. If the same force is applied to two objects of differ- ent mass, the heavier object has less acceleration than the lighter object (Figure 1).

How do you find acceleration example? ›

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction. Created by Sal Khan.

Can velocity be negative? ›

An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a positive acceleration).

What is SI unit of velocity? ›

The SI unit of velocity is metre per second (m/s).

Is velocity a vector? ›

Velocity is a vector quantity. As such, velocity is direction aware. When evaluating the velocity of an object, one must keep track of direction.

Is time a vector or scalar? ›

Time is neither vector nor scalar, it is a tensor.

Is displacement a scalar quantity? ›

No, displacement is a vector quantity. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.

Is force a vector or scalar? ›

Force is not a scalar quantity. Force is a vector quantity, as it has both direction and magnitude.

What is called a velocity? ›

Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude.

What velocity means? ›

-ˈläs-tē plural velocities. : quickness of motion : speed. the velocity of sound. : the rate of change of position along a straight line with respect to time.

What is final velocity? ›

The final velocity of an object is equal to its initial velocity plus acceleration multiplied by the time it travelled, and can be given as: v = u + aΔt. where, v = final velocity.

What are the 4 equations for acceleration? ›

Equations of Motion
Velocityv, equals, u, plus, a, t,v=u+at
Displacement with positive accelerations, equals, u, t, plus, one half, a, t, squared,s=ut+21at2
Displacement knowing initial and final velocitiess, equals, one half, left bracket, u, plus, v, right bracket, t,s=21(u+v)t
1 more row

What is Newton's formula for acceleration? ›

Newton's second law of motion is F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration.

What are the 3 formulas for velocity? ›

The three equations are, v = u + at. v² = u² + 2as. s = ut + ½at²

What are the 3 laws of motion formula? ›

In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

What is Newton's 2nd law of force and acceleration? ›

Force = mass X acceleration or F = ma. The law states that the acceleration of an object depends on the mass of the object and the amount of force applied. Newton's second law of motion is also called the law of force and acceleration.

What is Newton's 2nd law called? ›

The other name for Newton's second law is the law of force and acceleration.

What is acceleration in Newton's 2nd law? ›

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force.


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