# Physics Linear Motion (Part 2)

## Physics Linear Motion (Part 2)

### Physics Linear Motion (Part 2)

Equation of motion of freely falling bodies:

During a free fall the equations of motion as follows:

(a) Final velocity:

*v = v _{0 }+ gt*

*… … … (1)*

*or, v = 0 + gt*

*∴** v = gt … … … (2)*

(b) Distance:

*h= v _{0}t + *

*½ gt*

^{2}… … … (3)*or, h= 0 + **½ gt ^{2}*

*∴**h= **½ gt ^{2} … … (4)*

(c) Relation between final velocity and distance:

*v ^{2} = v_{0}^{2} + 2gh… … … (5)*

*or, v ^{2} = 0 + 2gh*

*∴** v ^{2} = 2gh … … (6)*

**Equation of motion of a body through vertically upward are as follows:**

*v = v _{0 }– gt*

*… … … (7)*

*h= v _{0}t – *

*½ gt*

^{2}… … … (8)*v ^{2} = v_{0}^{2} – 2gh… … … (9)*

**Maximum height: **At the maximum height the velocity of the body becomes zero.

Let, the maximum height be *H*.

And the initial velocity, *v _{0}*

Final velocity at the maximum height *v = 0*

We know,

*v ^{2} = v_{0}^{2} – 2gH*

*or, 0 = v _{0}^{2} – 2gH*

Time to reach the maximum height:

Let, the time to reach maximum height be = *t _{1}*

∴ We get,

*v = v _{0 }– gt_{1}*

*or, 0 = v _{0 }– gt_{1}*

### Physics *Linear Motion* (Part 2)

**Time to reach the ground from maximum height:**

Let, the maximum height be = *H *and the required time to reach the ground be t_{2}

At the maximum height, *v = 0*

So, using equation (4) we can write

We see from (11) and (12)

*t _{1 }= t_{2}*

I.e. Time of ascending = Time of falling

#### Time of flight: Total time to flight:

Let, T = Time of ascending + Time of falling

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**Physics Linear Motion (Part 2)**

*Physics Linear Motion (Part 2)*

Physics Linear Motion (Part 2)

Physics Linear Motion (Part 2)

Physics Linear Motion (Part 2)