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# Motion

## 04 Acceleration

Acceleration of a body is defined as the rate of change of its velocity with time.

Acceleration can be represented as:

where v is the final and u is the initial velocity.

Objects moving around do not always do so at a constant speed, or in a constant direction. For example, planets revolving around the sun change their direction at every point, cars moving on a road subjected to traffic have different speeds at different point of time. Whenever we want a car to hurry up, we notice that its velocity increases. It is mathematically defined as rate of change of velocity.

Acceleration can also be interpreted from Newton’s second law which gives:

Where, is the net external force acting on the body,

a is acceleration and

m is the mass of the body.

So a body is accelerated only if net external force acts on the body and the acceleration produced in inversely proportional to mass.

Acceleration can be positive or negative depending on the direction of velocity.

When both act in the same direction then it is said as positive or the velocity of the body increases. For example, pressing the accelerator pedal of the vehicle increases the velocity.

Similarly when they act in opposite directions the acceleration is said to be negative or the velocity decreases. Example is, pressing the braking pedal of a vehicle so that the velocity decreases.

#### TYPES OF ACCELERATION

Acceleration can also be classified into two types:

• Uniform and
• Non – Uniform

#### UNIFORM ACCELERATION

• If an object travels in a straight line and its velocity changes by equal amounts in equal intervals of time, however small these intervals may be, the object is said to be in ‘uniform acceleration’.
• In other words, a body has a uniform acceleration if its velocity changes at a uniform rate.
• If the acceleration remains constant for a given interval of time it is said to be uniform.
• Equations of motion are applicable to uniform acceleration only.
• Some examples of the uniformly accelerated motion:
• The motion of a freely falling body
• The motion of a bicycle going down the slope of a road when the rider is not pedalling and wind resistance is negligible
• The motion of a ball rolling down an inclined plane.
• When body accelerates in a circular motion, with constant speed, the direction changes, causing change in velocity. Thus, acceleration or rate of change of velocity changes.

#### NON-UNIFORM ACCELERATION

• A body has a non-uniform acceleration if its velocity increases by unequal amounts in equal intervals of time.
• If acceleration changes in the given time interval, it is said to be non – uniform.

#### RETARDATION (OR DECELERATION OR NEGATIVE ACCELERATION)

If the velocity of a body increases, the acceleration is positive, and if the velocity of a body decreases, the acceleration is negative.

#### Concepts of density and specific gravity

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