# What is acceleration? (article) | Khan Academy (2023)

## What does acceleration mean?

Compared to displacement and velocity, acceleration is like the angry, fire-breathing dragon of motion variables. It can be violent; some people are scared of it; and if it's big, it forces you to take notice. That feeling you get when you're sitting in a plane during take-off, or slamming on the brakes in a car, or turning a corner at a high speed in a go kart are all situations where you are accelerating.

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.

If you’re not changing your speed and you’re not changing your direction, then you simply cannot be accelerating—no matter how fast you’re going. So, a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration, even though the jet is moving really fast, since the velocity isn’t changing. When the jet lands and quickly comes to a stop, it will have acceleration since it’s slowing down.

[Wait, what?]

Or, you can think about it this way. In a car you could accelerate by hitting the gas or the brakes, either of which would cause a change in speed. But you could also use the steering wheel to turn, which would change your direction of motion. Any of these would be considered an acceleration since they change velocity.

[Huh?]

## What's the formula for acceleration?

To be specific, acceleration is defined to be the rate of change of the velocity.

$\Huge{a=\frac{\Delta v}{\Delta t} = \frac {v_f-v_i}{\Delta t}}$a=ΔtΔv=Δtvfvia, equals, start fraction, delta, v, divided by, delta, t, end fraction, equals, start fraction, v, start subscript, f, end subscript, minus, v, start subscript, i, end subscript, divided by, delta, t, end fraction

The above equation says that the acceleration, $a$aa, is equal to the difference between the initial and final velocities, $v_f - v_i$vfviv, start subscript, f, end subscript, minus, v, start subscript, i, end subscript, divided by the time, $\Delta t$Δtdelta, t, it took for the velocity to change from $v_i$viv, start subscript, i, end subscript to $v_f$vfv, start subscript, f, end subscript.

[Really?]

Note that the units for acceleration are $\dfrac{\text m/s}{\text s}$sm/sstart fraction, start text, m, end text, slash, s, divided by, start text, s, end text, end fraction , which can also be written as $\dfrac{\text m}{\text s^2}$s2mstart fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. That's because acceleration is telling you the number of meters per second by which the velocity is changing, during every second. Keep in mind that if you solve $\Large{a= \frac {v_f-v_i}{\Delta t}}$a=Δtvfvia, equals, start fraction, v, start subscript, f, end subscript, minus, v, start subscript, i, end subscript, divided by, delta, t, end fraction for $v_f$vfv, start subscript, f, end subscript, you get a rearranged version of this formula that’s really useful.

$v_f=v_i+a\Delta t$vf=vi+aΔtv, start subscript, f, end subscript, equals, v, start subscript, i, end subscript, plus, a, delta, t

This rearranged version of the formula lets you find the final velocity, $v_f$vfv, start subscript, f, end subscript, after a time, $\Delta t$Δtdelta, t, of constant acceleration, $a$aa.

I have to warn you that acceleration is one of the first really tricky ideas in physics. The problem isn’t that people lack an intuition about acceleration. Many people do have an intuition about acceleration, which unfortunately happens to be wrong much of the time. As Mark Twain said, “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

The incorrect intuition usually goes a little something like this: “Acceleration and velocity are basically the same thing, right?” Wrong. People often erroneously think that if the velocity of an object is large, then the acceleration must also be large. Or they think that if the velocity of an object is small, it means that acceleration must be small. But that “just ain’t so”. The value of the velocity at a given moment does not determine the acceleration. In other words, I can be changing my velocity at a high rate regardless of whether I'm currently moving slow or fast.

To help convince yourself that the magnitude of the velocity does not determine the acceleration, try figuring out the one category in the following chart that would describe each scenario.

high speed, low acceleration A car flooring it out of a red light A car that is driving at a slow and nearly steady velocity through a school zone A car that is moving fast and tries to pass another car on the freeway by flooring it A car driving with a high and nearly steady velocity on the freeway

[Show me the explanation for the answer.]

I wish I could say that there was only one misconception when it comes to acceleration, but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive.

People think, “If the acceleration is negative, then the object is slowing down, and if the acceleration is positive, then the object is speeding up, right?” Wrong. An object with negative acceleration could be speeding up, and an object with positive acceleration could be slowing down. How is this so? Consider the fact that acceleration is a vector that points in the same direction as the change in velocity. That means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity. Mathematically, a negative acceleration means you will subtract from the current value of the velocity, and a positive acceleration means you will add to the current value of the velocity. Subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase.

[Explain.]

If acceleration points in the same direction as the velocity, the object will be speeding up. And if the acceleration points in the opposite direction of the velocity, the object will be slowing down. Check out the accelerations in the diagram below, where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up. Assuming rightward is positive, the velocity is positive whenever the car is moving to the right, and the velocity is negative whenever the car is moving to the left. The acceleration points in the same direction as the velocity if the car is speeding up, and in the opposite direction if the car is slowing down.

[I don't get it.]

Another way to say this is that if the acceleration has the same sign as the velocity, the object will be speeding up. And if the acceleration has the opposite sign as the velocity, the object will be slowing down.

## What do solved examples involving acceleration look like?

### Example 1:

A neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds.
What was the magnitude of the average acceleration of the tiger shark?

$a= \dfrac {v_f-v_i}{\Delta t} \qquad$a=Δtvfvia, equals, start fraction, v, start subscript, f, end subscript, minus, v, start subscript, i, end subscript, divided by, delta, t, end fraction

Plug in the final velocity, initial velocity, and time interval.

$a=\dfrac {12\frac{\text{m}}{\text{s}}-0\frac{\text{m}}{\text{s}}}{3\text{s}} \qquad$a=3s12sm0sma, equals, start fraction, 12, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, minus, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, divided by, 3, start text, s, end text, end fraction

Calculate and celebrate!

$a= 4\frac{\text{m}}{\text{s}^2} \qquad$a=4s2ma, equals, 4, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction

### Example 2:

A bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared.
What will the speed of the bald eagle be after the wind has blown for 3 seconds?

$a= \dfrac {v_f-v_i}{\Delta t} \qquad$a=Δtvfvia, equals, start fraction, v, start subscript, f, end subscript, minus, v, start subscript, i, end subscript, divided by, delta, t, end fraction

Symbolically solve to isolate the final velocity on one side of the equation.

$v_f=v_i +a \Delta t \qquad$vf=vi+aΔtv, start subscript, f, end subscript, equals, v, start subscript, i, end subscript, plus, a, delta, t

Plug in the initial velocity as negative since it points left.

$v_f=-34\dfrac{\text{m}}{\text{s}} +a \Delta t \qquad$vf=34sm+aΔtv, start subscript, f, end subscript, equals, minus, 34, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, plus, a, delta, t

[Why negative?]

Plug in acceleration with opposite sign as velocity since the eagle is slowing.

$v_f=-34\dfrac{\text{m}}{\text{s}} + 8\dfrac{\text{m}}{\text{s}^2} \Delta t \quad$vf=34sm+8s2mΔtv, start subscript, f, end subscript, equals, minus, 34, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, plus, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction, delta, t

[What?]

Plug in the time interval during which the acceleration acted.

$v_f=-34\dfrac{\text{m}}{\text{s}} + 8\dfrac{\text{m}}{\text{s}^2} (3\text{s}) \qquad$vf=34sm+8s2m(3s)v, start subscript, f, end subscript, equals, minus, 34, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, plus, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction, left parenthesis, 3, start text, s, end text, right parenthesis

Solve for the final velocity.

$v_f=-10\dfrac{\text{m}}{\text{s}} \qquad$vf=10smv, start subscript, f, end subscript, equals, minus, 10, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction

The question asked for speed; since speed is always a positive number, the answer must be positive.

$\text{final speed}= +10\dfrac{\text{m}}{\text{s}} \quad$finalspeed=+10smstart text, f, i, n, a, l, space, s, p, e, e, d, end text, equals, plus, 10, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction

Note: Alternatively we could have taken the initial direction of the eagle's motion to the left as positive, in which case the initial velocity would have been $+34\dfrac{\text m}{\text s}$+34smplus, 34, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, the acceleration would have been $-8\dfrac{\text{m}}{\text{s}^2}$8s2mminus, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction, and the final velocity would have come out to equal $+10\dfrac{\text{m}}{\text{s}}$+10smplus, 10, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. If you always choose the current direction of motion as positive, then an object that is slowing down will always have a negative acceleration. However, if you always choose rightward as positive, then an object that is slowing down could have a positive acceleration—specifically, if it is moving to the left and slowing down.

## FAQs

### What is the difference between acceleration and velocity Khan Academy? ›

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction—or change both.

What is acceleration explained? ›

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.

What does acceleration mean in ELA? ›

Acceleration is an intervention that moves students through an educational program at a more rapid rate than their age-mates.

What does acceleration mean in a class? ›

In education, the term acceleration refers to a wide variety of educational and instructional strategies that educators use to advance the learning progress of students who are struggling academically or who have fallen behind—i.e., strategies that help these students catch up to their peers, perform at an expected ...

What is the main difference between acceleration and velocity? ›

Difference between Velocity and 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.

What is acceleration and why its important? ›

Acceleration ability shows the rate of change of velocity of an athlete in a time interval or in a definite distance, thus starting from rest how fast they reach their maximal or submaximal speed. It is a very important ability for sprinters and in all ball games.

What are the 4 types of acceleration? ›

There are three types of accelerated motions : uniform acceleration, non-uniform acceleration and average acceleration.

What is acceleration for dummies? ›

What is acceleration? Acceleration is the measurement of change in an object's velocity. When you press down on the gas pedal in a car, the car surges forward going faster and faster. This change in velocity is acceleration.

What are 5 examples of acceleration? ›

Some positive acceleration examples are given below:
• Launching a rocket.
• Accelerating a vehicle.
• A free falling object.
• Pedaling a bicycle.
• Rowing a boat.
• Airplane take off.

What is an example of acceleration in the classroom? ›

Subject-matter acceleration or partial acceleration may be accomplished by the student either physically moving to a higher-level class for instruction (e.g., a second-grade student going to a fifth-grade reading group), using time outside of the general instructional schedule (e.g., summer school or after school), or ...

### What is an example of acceleration in school? ›

Concurrent/Dual enrollment. In this form of acceleration, students take a course at one level and receive concurrent credit for a parallel course at a higher level. For example, a student may take algebra at the middle school, and earn credit at both the middle school and high school level.

What is the purpose of acceleration in education? ›

Acceleration refers to an instructional strategy that aims to help students who have fallen behind to meet or exceed grade-level learning standards.

Why is acceleration a gifted student? ›

Most students recommended for acceleration perform well above grade level prior to their accelerated placement. Research on acceleration indicates that students properly accelerated are capable of quickly catching up to their academic- level peers and that any gaps in knowledge quickly disappear.

Is acceleration good for students? ›

In addition, researchers have found that, overall, acceleration influences high-ability students' academic achievement in positive ways, and that these students outperform peers in other areas, including scores on standardized tests, grades in college, and the status of the universities they attend and their later ...

What are three examples of acceleration? ›

Examples
• 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 three ways an object can accelerate? ›

Objects can accelerate, or change their rate of velocity, in one of three ways. They can accelerate as a result of a change in speed. They can accelerate in response to a change in direction. Finally, they can accelerate as a result of changes in both speed and direction.

How does speed affect acceleration? ›

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 is the unit used for acceleration? ›

Unit of acceleration is the metre per second per second (m/s2). Definition. The snewton is that force which, when acting on a mass of one kilogramme, produces an acceleration of one metre per second per second. Force = mass × acceleration 1(N) = 1 ( kg ) × 1 ( m/s 2 ) .

Is acceleration related to speed? ›

When an object changes speed or direction, we call this acceleration. Acceleration is the rate at which velocity changes. Remember, velocity has two components: speed and direction.

Why is acceleration more important than velocity? ›

In terms of running, anytime the body starts, speeds up, or changes direction, it is accelerating. Given the number of direction changes in most sports, together with the number of times the rate of velocity needs to change, then clearly acceleration plays a crucial role in speed performance in sport.

### Which best describes 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.

What are 3 important facts about acceleration? ›

Acceleration has to have speed and direction and a rate of change of speed. Constant acceleration is when an object is changing its velocity at the same rate each second. Acceleration direction depends on whether the object is speeding up or slowing down. A free falling object falls because of gravity acting on it.

What is a real life 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 car's motion.

What are the 2 kinds 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 are the 2 formulas for acceleration? ›

Acceleration formula – three acceleration equations
• a = (v_f - v_i) / Δt ;
• a = 2 × (Δd - v_i × Δt) / Δt² ;
• a = F / m ;
Feb 2, 2023

Are there 3 types of acceleration? ›

Mainly, Uniform acceleration, non-uniform acceleration, and average acceleration are the three types of accelerated motions. The term uniform acceleration refers to a motion wherein an object travels in a straight line with an increase in velocity at equal intervals of time.

What is a simple example of acceleration? ›

The change in the velocity of an object could be an increase or decrease in speed or a change in the direction of motion. A few examples of acceleration are the falling of an apple, the moon orbiting around the earth, or when a car is stopped at the traffic lights.

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 is one benefit of acceleration for schools? ›

Increased Student Success

This increases student confidence and creates a more positive experience as they engage in productive struggle with appropriately challenging tasks. Thus, accelerated learning increases student success by preparing students for learning of new content.

What are the types of academic acceleration? ›

Types of Acceleration Identified in A Nation Empowered:

Grade-skipping (or whole-grade acceleration) Continuous progress. Self-paced instruction. Subject-matter acceleration/partial acceleration (Or content-based acceleration)

### What are the cons of acceleration for gifted students? ›

They cause trouble by talking to peers, fidgeting, and asking too many questions. They don't learn study skills, avoid taking academic risks, and may become underachievers.

What is the difference between accelerated and gifted? ›

Acceleration just means moving more quickly through the stages of the curriculum. So, if during a typical year, a typical student would do levels one through three of a subject, gifted kids would get through four levels, and end the year ahead of their age peers.

How rare are gifted students? ›

0.13% of the population is more than three standard deviations below the mean (IQ <55), and 0.13% of the population is more than three standard deviations above the mean (IQ 145-160). Thus, 13 out of 10,000 individuals score above 145 and are considered profoundly gifted.

What is the difference between velocity and acceleration quizlet? ›

What is the difference between velocity and acceleration? Velocity is how fast an object moves and acceleration is the rate of change in velocity.

How do velocity and acceleration differ from one another _____? ›

Velocity is the rate of change of position with respect to time, whereas acceleration is the rate of change of velocity. Both are vector quantities (and so also have a specified direction), but the units of velocity are meters per second while the units of acceleration are meters per second squared.

What is velocity and acceleration 8th grade? ›

When the velocity of an object changes, the object is accelerating. Velocity can be either a change in how fast something is moving, or a change in direction. An object changes its speed, direction, or both. The acceleration is in the same direction as the velocity, the speed increases and the acceleration is positive.

What is the relationship between acceleration and velocity? ›

Acceleration is the rate of change of velocity. (when velocity changes -> acceleration exists) If an object is changing its velocity, i.e. changing its speed or changing its direction, then it is said to be accelerating. Acceleration = Velocity / Time (Acceleration)

What is acceleration as a relationship between velocity and time? ›

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.

What is the relationship between acceleration speed and velocity? ›

When an object changes speed or direction, we call this acceleration. Acceleration is the rate at which velocity changes. Remember, velocity has two components: speed and direction.

What happens to acceleration when velocity stays the same? ›

Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating.

### Can acceleration change and velocity remain the same? ›

Yes. Even though the initial and final speeds are the same, there has been a change in direction for the object. Thus, there is an acceleration. The object was moving rightward and slowed down to 0 m/s before changing directions and speeding up while traveling leftward.

How do you determine the acceleration of an object? ›

Summary
1. According to Newton's second law of motion, the acceleration of an object equals the net force acting on it divided by its mass, or a = F m .
2. This equation for acceleration can be used to calculate the acceleration of an object when its mass and the net force acting on it are known.
Feb 26, 2022

What is acceleration for Grade 8? ›

An object is said to be accelerated if there is a change in its velocity. The change in the velocity of an object could be an increase or decrease in speed or a change in the direction of motion.

How do you explain acceleration to a child? ›

Acceleration is the measurement of change in an object's velocity. When you press down on the gas pedal in a car, the car surges forward going faster and faster. This change in velocity is acceleration.

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