Subject: Science

Acceleration is defined as the change in velocity per unit time. The negative acceleration is called retardation or deceleration. This note provides us with an information about acceleration and retardation.

Acceleration is defined as the change in velocity per unit time. Acceleration is measured in m/s^{2}.

=

**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/s^{2}

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/s^{2}

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 at^{2}………………. (iii)

This is the third equation of motion.

- 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.

Define acceleration.

^{2}.

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

Solution

Initial velocity (u) = 0

Final velocity (v) = 10 m/s

Time taken (t) = 5 s

Acceleration (a) =?

Or,

Or,

∴ a = 2m/s^{2}

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

Solution:

Initial velocity (u) = 0

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

Acceleration (a) = 0.3 m/s^{2}

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

Derive first equation of motion.

Solution:

Or,

Or, at = v-u

∴ v= u + at ………….. (i)

This is the first equation of motion.

Derive second equation of motion.

Or,

Or,

Or,

As both, equation is equal

Or,

Or, 2s = (u + v)t

∴ ……………… (ii)

This is the second equation of the motion.

Derive third equation of motion.

Solution:

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 at^{2}………………. (iii)

This is the third equation of motion.

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