What is Acceleration: When there is a change in the velocity of an object, it is called acceleration. Velocity is known to be a vector quantity with both magnitude and direction. So, we can say that acceleration occurs when there is a change in the direction or speed of an object. We use the word acceleration in our everyday lives.

To accelerate an object is to change its velocity, which is accomplished by altering either its speed or direction (like in case of uniform circular motion) in relation to time. Acceleration can have positive and negative values. Any time that the sign (+ or -) of the acceleration is the same as the sign of the velocity, the object will speed up. If the signs are opposite, the object will slow down.

What is Acceleration?

Acceleration is defined as the rate of change of velocity. In other words, the change in velocity from initial to final in the unit time is what we call acceleration.

Imagine you are driving a car. Pressing the accelerator makes the car go faster. In some time we can notice velocity is increased to the higher velocity (final velocity) from the initial velocity.

If the velocity in the beginning was \(‘u’,\) and after \(‘t’\) seconds, it increased to velocity, \(‘v’,\) then this means that –

\({\rm{acceleration}}\left( a \right) = \;\frac{{{\rm{final\;velocity}}\left( v \right) – {\rm{initial\;velocity}}\left( u \right)}}{{{\rm{time}}\left( t \right)}}\)

Unit of Accelaration

The SI unit of velocity is metre per second \(\left( {{\rm{m}}\,{{\rm{s}}^{ – 1}}} \right).\) Unit of time is second (s). From the following formula
\({\rm{acceleration}} = \frac{{{\rm{velocity}}\left( {{\rm{m}}\,{{\rm{s}}^{ – 1}}} \right)}}{{{\rm{time}}\left( {\rm{s}} \right)}}\)
SI unit of acceleration is \({\rm{m}}\,{\mkern 1mu} {{\rm{s}}^{{\rm{ – 2}}}}\)
CGS unit of acceleration is \({\rm{cm}}\,{{\rm{s}}^{{\rm{ – 2}}}}\)

Acceleration as a Vector Quantity

A vector is a quantity that requires both magnitude (numerical value) and direction to completely describe it. Whereas a scalar required only magnitude to describe it. Speed is a scalar quantity, and velocity is a vector quantity.

This means that there will be acceleration:

1. if the velocity changes, or
2. if the direction changes even if the velocity remains constant, or
3. if both velocity and direction changes

The earth can be said to be accelerating because it is constantly changing di

Types of Acceleration

Different types of acceleration are discussed below in detail:

a. Uniform Acceleration

However small the time intervals are if an object achieves equal changes in the velocity in equal time intervals the object is said to be moving with uniform acceleration. For example, velocity-time graph of an object moving on a straight line is as follows:

In the period between \(20\) and \({\text{40 s}}\), the velocity has increased from \(25\,{\rm{m}}\,{{\rm{s}}^{ – 1}}\) to \(35\,{\mkern 1mu} {\rm{m}}\,{{\rm{s}}^{ – 1}}.\) Similarly, from \(20\) to \({\text{40 s}}\), velocity rose from \(35{\mkern 1mu} \,{\rm{m}}\,{{\rm{s}}^{ – 1}}\) to \(45{\mkern 1mu} \,{\rm{m}}\,{{\rm{s}}^{ – 1}}.\) Acceleration is constant at \(0.5\,{\mkern 1mu} {\rm{m}}\,{{\rm{s}}^{ – 1}}.\)
We can also conclude that, for uniformly accelerating objects, the velocity time graph gives a straight line. And the slope of such graph gives the acceleration of the object.

b. Non-uniform Acceleration

Depending on the road conditions and traffic, a vehicle does not move with constant velocity. It accelerates sometimes or it uses brakes sometimes. This causes acceleration to vary. So, it is also called variable acceleration.

The velocity is sometimes increasing, sometimes decreasing. The change in the velocity is random for time intervals. This makes the acceleration non-uniform.

Relation Between Force and Acceleration

Force means the push or pull on objects. A force can move, increase speed, decrease speed, change direction, stop a moving object, or change the shape of an object. So, there is a direct relation between force and acceleration.

By Newton’s second law of motion, the resultant force on any object is the product of its mass and acceleration.

\({\rm{Resultant}}\,{\rm{Force}}\, = \,{\rm{mass}}\, \times \,{\rm{acceleration}}\)

Acceleration and Direction

As we have already learned that the acceleration is a vector quantity, if its direction is opposite to the reference positive direction, we call it negative acceleration. For example, if we consider, vertically upwards direction as positive, then for aly falling object, acceleration due to gravity will be negative as it is opposite the reference direction.

If we consider the same example, and now if we take vertically downwards as positive, the acceleration due to gravity will be positive as its direction is along the reference direction.

The positive or negative value of acceleration quantity does not tell if the object is speeding up or slowing down. The magnitude along with direction is taken together to know if it is speeding up or slowing down.

Observe the following situations.

i. Directions right of origin and top of origin (upward direction) are taken as positive.
ii. Directions left of the origin and below origin (downward direction) are taken as negative.

1. In the top left picture, acceleration of the cyclist is negative, as it is opposite to the reference direction. His velocity is towards right which is positive, but it decreases with time as its acceleration is towards left.
2. In the top right picture, acceleration of the cyclist is positive. As his velocity is also towards right his speed increases with time.
   Similar interpretations can be made for the bottom left and bottom right picture.

Deceleration vs Negative Acceleration 

Deceleration and negative acceleration are not the same. In deceleration, the body always slows down. Braking of a vehicle to slow it down is an example of deceleration. But in negative acceleration, the body may slow down or even speed up, as seen from the above table.

Velocity – Time Graph

1. The slope of the tangent drawn at any point to the velocity-time graph gives the acceleration of motion at that instant.
   i) From the above graph we can observe that from point a to point c, the slope is decreasing. Its value is zero at point b and negative at point c.
   ii) Hence acceleration is also decreasing with time. It becomes zero at point b and becomes negative after that.
2. The Velocity-time graph of a uniformly accelerating motion will be a straight line. The slope of such a line gives the uniform acceleration with which the object is moving.
3. The Velocity-time graph of an object moving with constant velocity will be a horizontal straight line. The slope of such a line is zero, and hence acceleration is also zero.

What is Acceleration Due to Gravity

This refers to the acceleration of objects fallingly in the Earth’s gravity. If an object is moving towards earth, at each instant, the velocity increases at a constant rate. So, it is a uniform acceleration. The value of acceleration (downwards) of any objectly falling near Earth’s surface is

\(g = 9.81\,{\mkern 1mu} {\rm{m}}\,{{\rm{s}}^{ – 2}}\)

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