Acceleration

Acceleration is the rate of change of velocity of a moving object, whether in a straight line or a curved or circular motion. This change of velocity is measured in meters per second per second, expressed as m/s². Acceleration occurs any time there is a change in speed or direction. It includes slowing down (negative acceleration) as well as speeding up. Because it involves both speed and direction, acceleration is a vector quantity.

Overview

Galileo Galilei (1564–1642), an Italian physicist, experimented with the velocity of objects by rolling them down an inclined plane. Velocity is the rate of change in an object’s position. Galileo observed that the objects gained speed as they rolled. He conducted a long-term study of the distances objects rolled and the time it took them to roll this distance. He eventually was able to show that each distance was in proportion to the time squared. For example, a ball that reaches a speed of 0.5 meters per second in 10 seconds has an acceleration rate of 0.05 m/s². He wrote the mathematical equation to describe how the velocity of the objects increased as they rolled—a quantitative description of uniformly accelerated motion.

Although the first descriptions of velocity came from Galileo, Sir Isaac Newton (1642–1727), an English physicist, took the next step and explained that some force must act upon an object to increase its velocity. For the rolling objects (or falling apples), the force was gravity. Newton’s First Law of Motion states that unless an external force acts upon them, objects at rest remain at rest and objects in motion at a constant velocity continue in their direction at the same velocity.

Newton’s Second Law of Motion applies to acceleration. It states that the sum of all forces (F) acting on an object is equal to the mass (m) of the object multiplied by the acceleration (a) of the object, or F = ma. That means that acceleration occurs when a force affects an object or mass, and the greater the mass, the greater the force needed to cause acceleration. In other words, more force is required when moving heavier objects the same distance as lighter ones. For example, a person can kick a hollow plastic ball a considerable distance without much effort but would need substantial strength to push a rock of similar size the same distance.

Acceleration changes either the speed or the direction of an object. Accelerometers are devices that measure acceleration. They are used in smartphones, tablets, smart watches, and other electronic devices to detect motion and changes in orientation. A car that pulls onto a street is accelerating as long as it is gaining speed; once the speed levels off and becomes constant, it is no longer accelerating. However, if it rounds a curve that changes its direction, it is then accelerating, even if the speed remains constant. Deceleration occurs when the car slows down.

Linear Acceleration

The term linear acceleration refers to a change in velocity without a change in direction—the object travels in a straight line. When an object moves in one direction for a given time, such as a car driving on a straight highway, it is accelerating only if its speed varies. For example, if the car is traveling at 26 m/s west (about 58 mph) and speeds up to 31 m/s west (about 69 mph), it is accelerating. But it is also accelerating if it slows to 14 m/s west (about 31 mph) when a deer crosses the road. Linear acceleration is expressed as a positive number if the car is speeding up and as a negative number if it is slowing down.

Centripetal Acceleration

When an object rotates, or moves in a circular pattern, it changes velocity even though its speed does not change. The velocity is tangent to the circle and, because acceleration is always perpendicular to the velocity, the direction of the acceleration is toward the center of the circle. Thus, it is called centripetal acceleration. The force providing the acceleration can be the tension in a string, if the object is a tethered ball, or gravity if it is a moon orbiting a planet. The formula for calculating such circular acceleration is a = v²/r.

G Force

G force is measured in relation to the gravitational pull present on Earth’s surface. Standard gravity is 1 g, or 9.80665 m/s². Forces above 1 g cause the sensation of carrying greater weight. High g forces can be caused by sudden acceleration. Human tolerance to g forces depends on the magnitude, duration, and direction of the acceleration; sustained high g forces can cause loss of consciousness, severe injury, or death.

The greatest force scientists have produced involves centrifuges, which spin materials at high speed, reaching g forces of several hundred thousand. The force can be strengthened further if the acceleration takes place in a circular pattern. For example, people riding in an airplane experience a mildly increased g force at takeoff, but a jet pilot flying in a tight circular pattern at a high speed will feel a pull about 10 times greater than normal gravity. Part of the thrill of roller coasters is the increased g forces produced by speed and sudden curves. Researchers studying microscopic fluid vortices reported accelerations exceeding one million times the force of gravity.

Resistance

When an object is dropped, the force of gravity causes it to accelerate rapidly as it falls. However, as it falls, friction from the particles in the air reduces the acceleration. There is a point at which the force of resistance and the force of gravity balance out; after that, the object’s acceleration is zero, and it simply falls at what is called terminal velocity. Although it is true that falling objects of unlike mass accelerate at the same rate, those with large surface areas, such as parachutes, pick up more air resistance and reach terminal velocity more quickly.

Bibliography

“Circular Motion & Gravitation.” Introductory General Physics, 2013, ww2.odu.edu/~jdudek/Phys111N_materials/4_circular_motion_gravity.pdf. Accessed 5 June 2026.

“Device Sensors.” Apple Developer, developer.apple.com/documentation/technologyoverviews/device-sensors. Accessed 5 June 2026.

Felton, James. “Why Do We Feel Acceleration But Not Constant Speed?” IFL Science, 2 June 2024, www.iflscience.com/why-do-we-feel-acceleration-but-not-constant-speed-74479. Accessed 5 June 2026.

“Smallest Whirlpools Can Pack Stunningly Strong Force.” ScienceDaily, 4 Sept. 2003. www.sciencedaily.com/releases/2003/09/030904075438.htm. Accessed 5 June 2026.