Acceleration

In physics, acceleration measures how quickly an object's speed and direction of motion are changing. It tells us how fast the velocity of an object is changing. Acceleration, like velocity, has both a size and a direction, making it a vector quantity. The standard unit to measure acceleration is the metre per second squared (m⋅s⁻², m/s²).

Tangential acceleration is the part of acceleration that happens in the same direction as the object's motion. When an object moves in a straight line and its speed changes, this is called linear acceleration. Deceleration happens when acceleration is in the opposite direction to the object's motion. Radial or normal acceleration, also known as centripetal acceleration during circular motions, changes the direction of the object's velocity.

In Newtonian mechanics, acceleration happens because of forces acting on an object. The overall acceleration depends on the overall force acting on it. According to Newton's second law, the size of the acceleration is related to the size of the force and the mass of the object. The direction of the acceleration is the same as the direction of the overall force.

Definition and properties

Acceleration tells us how fast an object's speed or direction changes. It measures how much the velocity — the speed and direction of motion — changes each second.

There are two main ways to think about acceleration. The first is average acceleration, which looks at how much the velocity changes over a certain time. For example, if a car speeds up from 10 to 20 kilometers per hour in 5 seconds, its average acceleration can be found. The second is instantaneous acceleration, which looks at the exact change in velocity at any moment. This is more detailed but harder to measure.

Acceleration is important because it connects to forces. According to Newton's second law, the force acting on an object equals its mass times its acceleration. This helps us understand motion by studying acceleration and forces together.

Example

When a vehicle starts moving from a stop and goes faster in a straight line, it is speeding up, or accelerating, in the direction it is moving. If the vehicle turns, it also accelerates toward the new direction, changing how it moves. The part of this acceleration that matches the direction the vehicle is moving is called linear acceleration. People inside feel as if they are pushed back into their seats.

When the vehicle changes direction, another part of the acceleration works at a right angle to the motion. This is called radial or normal acceleration. People inside feel as if they are pushed outward. If the vehicle slows down, this is also a type of acceleration, but in the opposite direction of motion, sometimes called deceleration. People inside feel pushed forward. Both speeding up and slowing down are changes in velocity and are treated the same way. These changes in acceleration are felt by everyone inside until their speed matches the new motion.

Tangential and centripetal acceleration

See also: Centripetal force § Local coordinates

When something moves along a curved path, its speed and direction can change. This change in motion is called acceleration. There are two types of acceleration. Tangential acceleration happens when the speed changes. Centripetal acceleration happens when the direction changes, like when something moves in a circle.

Special cases

Uniform or constant acceleration is when an object's speed changes by the same amount in each time period.

A common example of uniform acceleration is an object in free fall in a uniform gravitational field. The acceleration of a falling body without any resistance depends only on the strength of the gravitational field. There are simple formulas that connect how far an object moves, its speed, and its acceleration over time.

In uniform circular motion, an object moves along a circle at a constant speed. Even though its speed does not change, its direction does, which means it is accelerating. This acceleration points toward the center of the circle and is needed to keep the object moving in a curved path. The strength of this acceleration depends on the object's speed and the size of the circle.

Coordinate systems

In Cartesian coordinate systems, acceleration can be split into parts that match each direction. In a two-dimensional system, with an x-axis and a y-axis, acceleration is described using two parts: one for the x-direction and one for the y-direction.

In a three-dimensional system, which adds a z-axis, there is an extra part for the z-direction. The total acceleration is described using all three parts together.

Relation to relativity

Special relativity

Special relativity explains how objects behave when they move close to the speed of light. At everyday speeds, the old rules of motion work very well. But as things go faster and faster, near the speed of light, these rules change. The faster an object goes, the less it will speed up from the same push, and it can get very close to the speed of light but never actually reach it.

General relativity

Main article: General relativity

Sometimes, it can be hard to tell if a force we feel is because of gravity or because we are speeding up. In fact, the effects of gravity and speeding up feel exactly the same. Albert Einstein noticed this and called it the equivalence principle. Only people who feel no forces at all, not even gravity, can be sure they are not speeding up.

Conversions