# 2.4 Acceleration

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• Define and distinguish between instantaneous acceleration, average acceleration, and deceleration.
• Calculate acceleration given initial time, initial velocity, final time, and final velocity.

In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration    , the greater the change in velocity over a given time. The formal definition of acceleration is consistent with these notions, but more inclusive.

## Average acceleration

Average Acceleration is the rate at which velocity changes ,

$\stackrel{-}{a}=\frac{\Delta v}{\Delta t}=\frac{{v}_{f}-{v}_{0}}{{t}_{f}-{t}_{0}},$

where $\stackrel{-}{a}$ is average acceleration, $v$ is velocity, and $t$ is time. (The bar over the $a$ means average acceleration.)

Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are ${\text{m/s}}^{2}$ , meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.

Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction . For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.

## Acceleration as a vector

Acceleration is a vector in the same direction as the change in velocity, $\Delta v$ . Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.

Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion . When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration    .

## Misconception alert: deceleration vs. negative acceleration

Deceleration always refers to acceleration in the direction opposite to the direction of the velocity. Deceleration always reduces speed. Negative acceleration, however, is acceleration in the negative direction in the chosen coordinate system . Negative acceleration may or may not be deceleration, and deceleration may or may not be considered negative acceleration. For example, consider [link] .

what is specific heat capacity of watee
what is mass
Siyanbola
@siyanbola Resistance to acceleration
Dillon
The specific heat capacity of water is 1 calorie/1C°/ for 1 gram of water . it means that number of calories required to raise the temperature of 1g of water from 15 to 16C° is 1.
Khalil
understood?
Khalil
I think it's 1 in joules/kgC
Dillon
Anderson where are you from?. . &. what is your qualification
Khalil
Anderson i think you are right
Khalil
Micheal
lawrence
what is acceleration
lawrence
rate of change of velocity is acceleration
Khalil
its amount of heat to raise the temlrature through one kelvin of substance .
ghulam
The amount of heat energy required to raise the température of water by 1K
Cffrrcvccgg
infact a it must be a unit mass of water
Cffrrcvccgg
approximately equal to 4184J/Kg/K
Cffrrcvccgg
Just got through thermodynamics last semester. Also a change in 1 degree in celcius is equivalent to a change in 1 degree kelvin
Dillon
Also it's 1J/kgK or 4.184 cal/gK or /gC
Dillon
I think, at least
Dillon
Anderson are you good in physics numerical problems . if yes... . then plz help me. i am good in physics theory but nill in numericals
Khalil
I can try, what's the problem? I may be busy soon but I will reply today or tomorrow
Dillon
Numericals 🙄
Khalil
4200kJ/kgk...
Trevor
J
Trevor
I am so dull in physics please I need help
i am Physics professor its my Whats app contct no 9203366398003
ghulam
i am Physics professor
ghulam
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ghulam
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ghulam
Thank God
Sharon
How do we begin sir
Sharon
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ghulam
i need help
Khamis
yes
ghulam
ghulam
Khamis Khan where are from you
ghulam
Am a Ghanaian
Sharon
But am in Nigeria
Sharon
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Sharon
I am in Nigeria, Surulere, Lagos to be precise. I am a physics teacher and can help you. join my google class or whatsapp class@ +2348174872896
fitzgerald
abrahampaye8864@gmail.com
abraham
lasisi
Me too
yusuf
Nigeria too
yusuf
ok
paul
lawrence
lawrence
physics professor 'Where are from you' lol
lasisi
In Inelastic collision cunculate the vilocity
elucidate
Usman
yes, find velocity (v) because the mass of two objects is decreased when stuck together. if the mass in the system increases than the velocity decreases respectively
Shii
explain how a body becomes electrically charged based on the presence of charged particles
induction
babar
induction
DEMGUE
definitely by induction
Raymond
induction
Raymond
induction
Shah
induction
Korodhso
please why does a needle sinks in water
DEMGUE
induction
Korodhso
induction
Auwal
what are the calculations of Newton's third law of motiow
what is dark matter
(in some cosmological theories) non-luminous material which is postulated to exist in space and which could take either of two forms: weakly interacting particles ( cold dark matter ) or high-energy randomly moving particles created soon after the Big Bang ( hot dark matter ).
Usman
if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
what is a galaxy
a galaxy is a type of phone e.g samsung galaxy there are diff types of samsung galaxy there is s5 s6 s7 s8 s9
lasisi
what isflow rate of volume
flow rate is the volume of fluid which passes per unit time;
Rev
flow rate or discharge represnts the flow passing in unit volume per unit time
bhat
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
incomplete question
lasisi
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
nehemiah
why is it proportional
i don't know
y
nehemiah
what are the relationship between distance and displacement
They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
Thanks a lot
Usman
I'm beginner in physics so I can't reason why v=u+at change to v2=u2+2as and vice versa
Usman
what is kinematics
praveen
kinematics is study of motion without considering the causes of the motion
Theo
The study of motion without considering the cause 0f it
Usman
why electrons close to the nucleus have less energy and why do electrons far from the nucleus have more energy
Theo
thank you frds
praveen
plz what is the third law of thermodynamics
third law of thermodynamics states that at 0k the particles will collalse its also known as death of universe it was framed at that time when it waa nt posible to reach 0k but it was proved wrong
bhat
I have not try that experiment but I think it will magnet....
Hey Rev. it will
Jeff
I do think so, it will
Chidera
yes it will
lasisi