ArticleslgStudy

physics

Acceleration

Acceleration is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Acceleration rather than just read about it. In short: In physics, acceleration is a measure of how fast and in what direction an object's speed and direction of motion are changing. It is defined as the rate of change of the velocity.

Acceleration — main illustration
Acceleration — illustration

Key takeaways

  • Acceleration belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Acceleration to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Acceleration from memory before moving on to harder problems.

Reference excerpt

In physics, acceleration is a measure of how fast and in what direction an object's speed and direction of motion are changing. It is defined as the rate of change of the velocity. Like velocity, acceleration has a magnitude and a direction, making it a vector quantity. The SI unit for acceleration is metre per second squared (m⋅s−2, m/s2). The tangential acceleration of an object is the component of the acceleration which is in the same direction as the motion (or tangential velocity) of the object. When the velocity of the object does not change direction, this is called linear acceleration. Deceleration or retardation, on the other hand, is the component of the acceleration in the opposite (or antiparallel) direction to the tangential velocity. Radial acceleration or normal acceleration (or centripetal acceleration during circular motions) is the component of the acceleration that changes the direction of the object's velocity. In Newtonian mechanics, the acceleration of a mass arises from forces acting on it, with its net acceleration being a result of the net force acting on it. By Newton's second law, the magnitude of the net acceleration will be proportional to the magnitude of the net force acting on the object and inversely proportional to the mass of the object, while the direction of the net acceleration will be the same as the direction of the net force.

Definition and properties

Average acceleration

An object's average acceleration a ¯ {\displaystyle {\bar {\mathbf {a} }}} over a period of time is its change in velocity, Δ v {\displaystyle \Delta \mathbf {v} } , divided by the duration of the period, Δ t {\displaystyle \Delta t} . Mathematically,

a ¯ = Δ v Δ t . {\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.} The average acceleration is the simplest way to measure acceleration, requiring only knowledge of the change in velocity and the change in time. In a strict sense, the average acceleration is the only true acceleration one is able to directly measure without appealing to an empirical law, meaning that it is the most fundamental form of acceleration measurement. The average acceleration is most often used to approximate the kinematics of an object by assuming that the velocity changes linearly with time. Over short time intervals, we can often assume that the acceleration is uniform, meaning acceleration a {\displaystyle \mathbf {a} } of the object will be exactly equal to the average acceleration a ¯ {\displaystyle {\bar {\mathbf {a} }}} (see subsection Uniform acceleration for details.) By Newton's second law of motion, the average acceleration is related to the average force f ¯ {\displaystyle {\bar {\mathbf {f} }}} on a particle of mass m {\displaystyle m} by,

f ¯ = m a ¯ . {\displaystyle {\bar {\mathbf {f} }}=m{\bar {\mathbf {a} }}.} This means that a measurement of the average acceleration is also a measurement of the average force (also known as impulse J = f ¯ {\displaystyle \mathbf {J} ={\bar {\mathbf {f} }}} .)

Instantaneous acceleration

Instantaneous acceleration is the limit of the average acceleration over an infinitesimal interval of time. In the terms of calculus, instantaneous acceleration is the derivative of the velocity vector with respect to time:

a = lim Δ t → 0 Δ v Δ t = d v d t = v ˙ . {\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}={\dot {\mathbf {v} }}.}

As acceleration is defined as the derivative of velocity, v, with respect to time t and velocity is defined as the derivative of position, x, with respect to time, acceleration can be thought of as the second derivative of x with respect to t:

… excerpt ends here. Continue reading the full article.

Illustrations

Acceleration illustration
Acceleration: Drag racing is a sport in which specially-built vehicles compete to be the fastest to accelerate from a standing start.
Drag racing is a sport in which specially-built vehicles compete to be the fastest to accelerate from a standing start.
Acceleration: Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
Acceleration: Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0 of Δv/Δt.
Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0 of Δv/Δt.
Acceleration: From bottom to top: an acceleration function a(t);the integral of the acceleration is the velocity function v(t);and the integral of the velocity is the distance function s(t).
From bottom to top: an acceleration function a(t);the integral of the acceleration is the velocity function v(t);and the integral of the velocity is the distance function s(t).

Worked examples

Example 1 — a first encounter with Acceleration

Start with the simplest possible case. Write down what Acceleration claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Acceleration before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Acceleration ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Acceleration

In research
Acceleration appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Acceleration in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Acceleration is common in secondary-school and first-year university syllabi. It links to neighbouring topics Acceleration, Dynamics (mechanics), Kinematic properties, so understanding it makes those chapters shorter.
In everyday life
Look for Acceleration outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Acceleration in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Acceleration means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Acceleration out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Acceleration in simple terms?

In physics, acceleration is a measure of how fast and in what direction an object's speed and direction of motion are changing. It is defined as the rate of change of the velocity.

Why does Acceleration matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Acceleration?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Acceleration.

Tags

  • Acceleration
  • Dynamics (mechanics)
  • Kinematic properties
  • Vector physical quantities

Keep exploring