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Acceleration

Last Updated : 22 Apr, 2024
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Acceleration is defined as the rate of change in velocity. This implies that if an object’s velocity is increasing or decreasing, then the object is accelerating. Acceleration has both magnitude and direction, therefore it is a Vector quantity. According to Newton’s Second Law of Motion, acceleration is defined as the ratio of the force applied to the object to the mass of the object. 

Let’s understand more about acceleration and related concepts like Acceleration Formula, its Unit, Types, Graphs, Solved Examples, and FAQs, in this article!

Table of Content

  • What is Acceleration?
  • Acceleration Formula
  • Unit of Acceleration 
  • Types of Acceleration 
  • Difference Between Uniform Acceleration and Non-Uniform Acceleration
  • Velocity-Time Graph
  • Difference Between Acceleration and Velocity
  • Examples on Acceleration

What is Acceleration?

Acceleration is defined as the rate of change of the velocity of an object with respect to time. An object is said to be accelerating or have the acceleration when its velocity is changing.

Acceleration can also be termed as the rate of change in velocity and the change over time. An acceleration vector’s magnitude tells us how much the velocity will change, while its direction tells us how the velocity will change i.e. whether the velocity is increasing or decreasing, the velocity vector is changing direction, or some combination of the three.

Acceleration can be positive, zero, or negative. In case the object’s velocity increases with time, it can be termed Positive Acceleration. In case the velocity is zero, it is termed Zero Acceleration, while the negative acceleration also known as retardation indicates a decrease in velocity with time.

Acceleration Definition

Acceleration Definition

Acceleration Formula

Mathematically, the change in the velocity of an object in motion is defined as, (v – u) where v and u are the final and the initial velocities.

Therefore, the acceleration of the object is given by,

Acceleration = Change in Velocity / Time Taken

a = (v – u) / t

where,

  • a is the Acceleration
  • v is the Final Velocity
  • u is the Initial Velocity
  • t is the Time Taken by Object

Unit of Acceleration 

  • It is a vector quantity, which is associated with both magnitude and direction. It is denoted by ‘a’. 
  • The unit of acceleration is meters per second squared or meters per second (the object’s speed or velocity) per second or m/s2.

Note: Dimensional Formula of Acceleration is [M0 L1 T-2]

Types of Acceleration 

Following are the different types of acceleration associated with an object,

  • Uniform Acceleration 
  • Non-Uniform Acceleration 
  • Average Acceleration
  • Instantaneous Acceleration

Now let’s learn about each type of acceleration in detail.

Uniform Acceleration

In case the velocity of an object changes in equal amounts during the same time interval, then the body is said to be in uniform acceleration.  In this case, neither the direction nor magnitude changes with respect to time. 

Uniform Acceleration

For Examples:

  • A ball rolling down the slope.
  • When a bicycle rider is riding the bicycle on a slope where both pedals are engaged.
  • A kid sliding down from the slider.
  • Motion of car with constant velocity, etc

Non-Uniform Acceleration

Variable acceleration is the velocity of the body that changes by varying amounts during the same time interval. Variable acceleration comes into the picture when the object’s direction or magnitude or both changes with respect to time.

Non-Uniform Acceleration

For Examples:

  • A car changing speed.
  • Uniform circular motion
  • The motion of the pendulum with changing speed

Average Acceleration

The average acceleration is defined as the change in velocity for a particular specified time interval. The average acceleration can be calculated for a time instance, as follows, 

av = Δ v / Δ t

av = (vf – vi) / (tf – ti)

where,

  • vf is the Final Velocity 
  • vi is the Initial Velocity
  • ti is the Initial Time
  • tf is the Final Time

Instantaneous Acceleration

In order to calculate the instantaneous acceleration, the average velocity can be computed between two points in time separated by Δt and let Δt approach zero. The result obtained is the derivative of the velocity function v(t), which is instantaneous acceleration. Mathematically,

[Tex]a(t)=\dfrac{d}{dt}v\left(t\right) [/Tex]

Thus, similar to velocity being the derivative of the position function, instantaneous acceleration is the derivative of the velocity function. We can show this graphically in the same way as instantaneous velocity. In (Figure), instantaneous acceleration at time t0 is the slope of the tangent line to the velocity-versus-time graph at time t0. We see that average acceleration given as,  

[Tex]\overline a=\dfrac{Δv}{Δt}[/Tex] 

Difference Between Uniform Acceleration and Non-Uniform Acceleration

The difference between Uniform and Non-Uniform acceleration is explained in the table added below,

Uniform Acceleration Vs Non-Uniform Acceleration

Characteristics

Uniform Acceleration

Non-uniform acceleration

Definition

Uniform acceleration is defined as the acceleration in which the object changes its velocity within equal intervals of time.

Non-uniform acceleration is defined as the acceleration in which the object changes its velocity within unequal intervals of time.

Graph of Velocity vs Time

It is a straight line with constant slope.

It is a curved line with changing slope.

Direction of acceleration

Direction remains constant throughout motion with respect to time.

Direction changes over time.

Example

Object in free fall experiences uniform acceleration.

The motion of the pendulum with changing speed.

Velocity-Time Graph

The curves indicate the velocity-time graph time is plotted along the x-axis and velocity is plotted along the y-axis. While finding displacement through the v – t graph, keep the sign under consideration.

  • When the velocity of the particle is constant, or acceleration is zero.
Velocity-Time Graph1
  • When the particle is moving with a constant acceleration and its initial velocity is zero.
Velocity-Time Graph2
  • When the particle is moving with constant retardation.
Velocity-Time Graph3
  • When the particle moves with non-uniform acceleration and its initial velocity is zero.
Velocity-Time Graph4
  • When the acceleration decreases and increases.
Velocity-Time Graph5
  • The total area enclosed by the time-velocity curve represents the distance travelled by a body.
Velocity-Time Graph6

Difference Between Acceleration and Velocity

Here are some important differences between Acceleration and Velocity,

Characteristics

Acceleration

Velocity

Definition

Acceleration is defined as the rate of change of velocity with respect to time.Velocity is defined as the rate of change of displacement with respect to time.

Symbol

It is usually represented by ‘a’.

It is usually represented by ‘v’.

Direction

Acceleration can be positive or negative, not zero.Velocity can be zero, positive or negative.

SI Unit

The SI unit of Acceleration is m/s2.The SI unit of velocity is m/s.

Formula

The formula for acceleration is,

Acceleration = Velocity / Time 

The formula for velocity is,

Velocity = Displacement /Time 

Example

A car accelerates from an absolute halt to a higher speed.

A car moving at 80 km/h in a eastward direction.

Related Articles,

  • Angular Acceleration
  • Acceleration-Time Graph 
  • Uniformly Accelerated Motion
  • Acceleration due to Gravity
  • Average Acceleration Formula
  • Acceleration Time Graphs
  • Angular Acceleration

Examples on Acceleration

Some examples explaining the concept of acceleration are,

Example 1: If a truck accelerates from 6 m/s to 10 m/s in 10 s. Calculate its acceleration.

Solution:

Given,

  • Initial Velocity, u = 6 m/s
  • Final Velocity, v = 10 m/s
  • Time taken, t = 10 s

We have to find Acceleration ‘a’

Acceleration, a = (v – u) / t

                        = (10 m/s – 6  m/s) / 10 s

                        = 0.4 m/s2

Thus, the acceleration of the truck is 0.4 m/s2.

Example 2: If a ball is released from the terrace of a building to the ground. If the ball took 6 s to touch the ground. Find the height of the terrace from the ground.

Solution:

Given,

  • Initial Velocity u = 0 {as the ball was at rest}
  • Time taken by the ball to touch the ground t = 6 seconds 
  • Acceleration due to gravity a = g = 9.8 m/s2
  • Distance traveled by stone = Height of bridge  = s

Distance covered by the ball from the terrace to the ground

[Tex]s=ut+\frac{1}{2}gt^2 [/Tex]

[Tex]s = 0 + \frac{1}{2} × 9.8 × 36 = 176.4 m [/Tex]

Therefore, 

Distance of the terrace from the ground is 176.4 m.

Example 3: If a man is driving the car at 108 km/h slow down and bring it to 72 km/h in 5 s. Calculate the retardation of the car?

Solution: 

Given,

  • Initial velocity, u = 108 km/h or [Tex]108\times\frac{5}{18}=30\ m/s [/Tex]
  • Final velocity, v = 72 km/h or [Tex]72\times\frac{5}{18}=20\ m/s [/Tex]
  • Time taken, t = 5 seconds

Therefore, acceleration is,

[Tex]\begin{aligned}a&=\dfrac{v\ -\ u}{t}\\ &=\frac{20\ -\ 30}{5}\\  &= -2\ m/s^2\end{aligned} [/Tex]

Negative sign shows retardation.

Example 4: If a car moves from rest and then accelerates uniformly at the rate of 7.5 m/s2 for 10 s. Find the velocity of the train in 10 s.

Solution:

Given,

  • Initial velocity u = 0 {as the car was at rest}
  • Acceleration a = 7.5 m/s2
  • Time t = 10 s

v = u + at

   = 0 + 7.5 × 10

   = 75 m/s

Example 5: If an object moves along the x-axis according to the relation x = 1 – 2t + 3t2, where x is in meters and t is in seconds. Calculate the acceleration of the body when t = 3s.

Solution:

Given,

  • x = 1 – 2t + 3t2

Velocity, v = dx/dt  

                = d/dt {1 – 2t + 3t2}

                = -2 + 6t

Therefore,

Acceleration a = dv/dt = d/dt {-2 + 6t}

a = 6 m/s2 



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      First Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body's Internal Energy. The First L
      8 min read
    • Second Law of Thermodynamics
      Second Law of Thermodynamics defines that heat cannot move from a reservoir of lower temperature to a reservoir of higher temperature in a cyclic process. The second law of thermodynamics deals with transferring heat naturally from a hotter body to a colder body. Second Law of Thermodynamics is one
      10 min read
    • Thermodynamic Cycles
      Thermodynamic cycles are used to explain how heat engines, which convert heat into work, operate. A thermodynamic cycle is used to accomplish this. The application determines the kind of cycle that is employed in the engine. The thermodynamic cycle consists of a series of interrelated thermodynamic
      15 min read
    • Thermodynamic State Variables and Equation of State
      The branch of thermodynamics deals with the process of heat exchange by the gas or the temperature of the system of the gas. This branch also deals with the flow of heat from one part of the system to another part of the system. For systems that are present in the real world, there are some paramete
      5 min read
    • Enthalpy: Definition, Formula and Reactions
      Enthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let's know more about Enthalpy in detail below. Enthalpy
      13 min read
    • State Functions
      State Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state fun
      7 min read
    • Carnot Engine
      A Carnot motor is a hypothetical motor that works on the Carnot cycle. Nicolas Leonard Sadi Carnot fostered the fundamental model for this motor in 1824. In this unmistakable article, you will find out about the Carnot cycle and Carnot Theorem exhaustively. The Carnot motor is a hypothetical thermod
      5 min read
    • Heat Engine - Definition, Working, PV Diagram, Efficiency, Types
      Heat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to
      14 min read

    Wave and Oscillation

    • Introduction to Waves - Definition, Types, Properties
      A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
      11 min read
    • Wave Motion
      Wave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
      12 min read
    • Oscillation
      Oscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation” originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
      8 min read
    • Oscillatory Motion Formula
      Oscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
      3 min read
    • Amplitude Formula
      The largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
      7 min read
    • What is Frequency?
      Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
      9 min read
    • Amplitude, Time Period and Frequency of a Vibration
      Sound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
      5 min read
    • Energy of a Wave Formula
      Wave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
      7 min read
    • Simple Harmonic Motion
      Simple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
      15+ min read
    • Displacement in Simple Harmonic Motion
      The Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
      10 min read

    Sound

    • Production and Propagation of Sound
      Have you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
      6 min read
    • What are the Characteristics of Sound Waves?
      Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
      7 min read
    • Speed of Sound
      Speed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
      12 min read
    • Reflection of Sound
      Reflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
      9 min read
    • Refraction of Sound
      A sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
      5 min read
    • How do we hear?
      Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
      7 min read
    • Audible and Inaudible Sounds
      We hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
      10 min read
    • Explain the Working and Application of SONAR
      Sound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
      8 min read
    • Noise Pollution
      Noise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
      8 min read
    • Doppler Effect - Definition, Formula, Examples
      Doppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
      7 min read
    • Doppler Shift Formula
      When it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
      3 min read

    Electrostatics

    • Electrostatics
      Electrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force. Electrostatic forces are non con
      14 min read
    • Electric Charge
      Electric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
      8 min read
    • Coulomb's Law
      Coulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
      9 min read
    • Electric Dipole
      An electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
      11 min read
    • Dipole Moment
      Two small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
      6 min read
    • Electrostatic Potential
      Electrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
      12 min read
    • Electric Potential Energy
      Electrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field. Sometimes electrical potential energy is confused with electric po
      15+ min read
    • Potential due to an Electric Dipole
      The potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
      7 min read
    • Equipotential Surfaces
      When an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
      8 min read
    • Capacitor and Capacitance
      Capacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
      11 min read
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