Acceleration and Retardation

Acceleration

Acceleration is defined as the change in velocity per unit time. Acceleration is measured in m/s².

=

Retardation

The negative acceleration is called retardation or deceleration. Its unit is same as acceleration.

Example:

1. Car starts from rest. After 5 seconds, its velocity becomes 10 m/s. Then find its acceleration.

Initial velocity (u) = 0

Final velocity (v) = 10 m/s

Time taken (t) = 5 s

Acceleration (a) =?

Or,

Or,

∴ a = 2m/s²

2. The Car which starts from the rest has an acceleration of 0.3 m/s2. After 1 minute what will be its acceleration? What is the distance travelled by car?

Initial velocity (u) = 0

Time taken (t) = 1 min= 1 × 60 s = 60 s

Acceleration (a) = 0.3 m/s²

Final velocity (v) =?

Distanced travelled (s) =?

According to formula, v= u+ at

Or, v = 0 + 0.3 × 60

V= 18 m/s

∴ s =540 m

Equation of motion of uniform acceleration

Equations involving displacement, initial velocity, final velocity, acceleration and time of the motion of a moving body are equations of motion.

Considering a body moving in a straight line with uniform acceleration is shown in the figure.

Let,

Displacement = s

Initial velocity = u

Final velocity = v

Acceleration = a

Time taken = t

Relation between u, v, a and t

Or,

Or, at = v-u

∴ v= u + at ………….. (i)

This is the first equation of motion.

Relation between u,s, v and t

Or,

Or, \(\text{Average Velocity}=\frac{\text{Total Displacement(s)}}{\text{Total Time Taken(t)}}\)

Or,

As both, equation is equal

Or,

Or, 2s = (u + v)t

∴ ……………… (ii)

This is the second equation of the motion.

Relation between s, u, a and t

We already have,

V= u + at………….. (i)

s = (u + v)t…………… (ii)

Putting value of v from equation (i) in (ii)

Or,

Or, s =

Or, s = 2u×t + at × t× ½

∴ s = ut + ½ at²………………. (iii)

This is the third equation of motion.

Things to remember

• Acceleration is defined as the change in velocity per unit time. Acceleration is measured in m/s2.
• The negative acceleration is called retardation or deceleration. Its unit is same as acceleration.
  
• Equations involving displacement, initial velocity, final velocity, acceleration and time of motion of a moving body are equations of motion.
  

• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.

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