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Overview

Acceleration is the rate of change in velocity of an object during a given duration of time. The SI unit for acceleration is the meter per second squared. Other units are also commonly used. Acceleration can be uniform, such as the acceleration of an object in free fall, or variable such as acceleration during driving.

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Acceleration is a very useful concept in designing, building, and driving vehicles. It is also important when predicting and preventing the effects of shock, a sudden acceleration or deceleration as a result of the impact.

Transamerica Pyramid in San Francisco. The strong framework of this building is resistant to torsional forces generated by seismic events.

Acceleration and Suspension

Accounting for shock can prevent accidents during earthquakes if buildings are constructed to withstand it. In places where earthquakes are common, such as Japan, buildings are constructed on special platforms that reduce acceleration and deceleration. The principle behind such construction is similar to suspension in vehicles. A simple suspension device is used on bicycles to minimize the discomfort due to acceleration and deceleration when moving on an uneven surface and to prevent damage. The suspension is used in bridges to minimize their acceleration caused by moving vehicles. It is useful in music studios, where the floor or the entire studio is floating, to minimize acceleration caused by surrounding vehicles, pedestrians, etc. If the house is already built without concern for professional soundproofing, and the musician wishes to make a home studio there, it is logistically difficult to add suspension to the studio. Some ways to prevent the acceleration of the building is to increase the room’s mass. Suspended ceilings are also a solution because they are not as costly as suspending the entire room, but prevent the ceiling from accelerating and transmitting noise from above.


Acceleration in Physics

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Newton’s Second Law

According to the Second Law in Newtonian mechanics, the force acting upon a body is equal to the product of its mass and acceleration, expressed by the formula F = ma, where F is the force, m is the mass, and a — the acceleration. A force acting upon a body changes the original velocity with which the body travels, by increasing or decreasing the velocity, that is accelerating or decelerating the object. The Second Law shows that this change in velocity or acceleration depends not only on the magnitude of the force, which pushes the body, but is also inversely affected by the mass of the body. That is, if the same force is applied to two objects A and B, where B is heavier, then B will also have smaller acceleration. This property is called inertia; it shows the predisposition of a body to resist change in acceleration.

Accelerating motorcycle. Tour de Beauce, 2010. Québec City

It is easy to see this at work in daily life. For example, motorcycle drivers wear heavy padding and helmets because if the motorcycle collides with a car, both the motorcycle and the rider will change their velocity faster, accelerating more than the car, because their combined mass is much less than that of the car. This can send the rider flying and result in severe injuries, while the driver of the car would likely be in a much safer environment. This is not the only reason for protective gear, but it is one of them. In another example, when throwing a tennis ball and a stone of roughly the same shape and size with the same force, the tennis ball will be propelled with greater acceleration, because it is lighter than the stone. This example does not take into account gravity; it is assumed that the initial force that pushes the ball and the stone is large enough to make gravity negligible.


Acceleration and Circular Motion

Cyclists are subjected to centripetal acceleration as they turn. Tour de Beauce, 2010. Québec City

An object that is moving along a circle with a constant linear speed experiences a change in velocity, because its direction changes. Thus, the object is accelerating. The direction of this acceleration is towards the rotation axis, and it is called centripetal. While the centripetal acceleration and force are acting towards the rotation axis, there is also another force that acts in the opposite direction according to Newton’s Third Law. It is called the centrifugal force. This force is what keeps the upside-down roller coaster rides safe, because it pushes the cars and the passengers out of the circle, against the rails.

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Acceleration and Gravity

Gravitational force is one of the major forces that acts on objects and affects their acceleration. For objects near the surface of the Earth, it pulls them towards the Earth. When no other forces act upon an object released above the ground, it is said to be in free fall. It falls with an acceleration of 9.80665 meters per second squared. This value is denoted as a constant g and can be used in calculating the weight of an object. Since F = ma according to the Second Newton’s Law, weight, which is the force acting upon the object, is the product of the object’s mass and g. The mass of the object can be calculated easily, thus the weight is also easy to find. It is important to remember that the common use of “weight” actually refers to mass.

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Free fall acceleration, also known as gravitational acceleration, differs for planets and astronomical bodies and is affected by their mass. For example, the gravity of the Sun is almost 28 times that of the Earth, of Jupiter — about 2.6 times greater, and of Neptune — about 1.1 times greater than that of the Earth. The gravity of other planets is smaller than that of the Earth, for example, Moon’s gravity is 0.17 of Earth’s gravity.

Acceleration in Vehicles

Acceleration Tests for Cars

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0 to 60 miles per hour (0 to 97 kilometers per hour) time is a measure of performance of a vehicle, which determines the time it takes the car to accelerate to 60 miles per hour. The metric system measures the acceleration for 0 to 100 kilometers per hour (0 to 62 miles per hour). Some of the cars with the fastest acceleration reach it in approximately 2.3 seconds, which is less than 2.73 seconds in the 0-60 mph test for objects in free fall. There are even smartphone applications that help perform this test using phone’s accelerometers, although it is unclear how accurate they are.

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The Effect of Acceleration on People

When a vehicle accelerates, the passengers are pulled in the opposite direction of the acceleration, backward during acceleration and forward during deceleration. During a sudden stop, for example, due to an impact, passengers are pulled forward so much that they may fly out of their seats and hit the interior of the car, the windows, or even break the windows and fly outside. This is very dangerous, therefore seat belts are installed in all modern cars and most countries enforce the law that requires the driver, all children, and at least the passenger in the front seat to wear a seat belt.

During space travel, acceleration has to be extremely high to take the spacecraft to the orbit of the Earth. Conversely, on the way back to Earth, astronauts experience great deceleration. This is very uncomfortable and dangerous for the astronauts, therefore they have to undergo rigorous training in preparation for the flight, to raise their tolerance to high levels of acceleration. This is called high-G training. Some pilots and crew of high-speed aircraft also have to do this training due to high acceleration they experience. High acceleration draws blood away from the brain and this may result first in the loss of color vision, then peripheral vision, then all vision, and finally loss of consciousness. This is dangerous because pilots become unable to control the aircraft. Until the high-G training became routine, there were several fatal accidents due to the lack of tolerance to high acceleration. High-G training allows the brain to get used to these extreme accelerations for longer periods of time and prevents people from becoming unconscious.

Inside the Apollo capsule CM-011A aboard the aircraft carrier USS Hornet (CV-12)

Astronauts and pilots practice a “g-straining maneuver” of tensing the abdominal muscles. This makes the abdominal blood vessels smaller and makes it more difficult for blood to travel to the lower part of the body. They also wear g-suits to lessen the effects of extreme acceleration on the body. These suits are designed to restrict the blood flow to the lower body during acceleration, by applying pressure to the lower part of the body and the abdomen. This is usually achieved by air or liquid filled pockets that exert pressure on the body. To increase tolerance, astronauts and pilots train in human centrifuges that simulate high acceleration conditions. These centrifuges are long tubes, with the pilot’s cabin at one end. They are rotated in the horizontal plane to produce acceleration. During training, doctors monitor the pilot’s vital signs such as heart rate to ensure safety and track their tolerance. Centrifuges have different modes, simulating normal reentry and launch as well as ballistic reentry in emergency situations when a spacecraft cannot be controlled. Trainees who used the centrifuge report extreme discomfort in their chest and throat.