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 = v₀ + gt… … … (1)

or, v = 0 + gt

∴ v = gt … … … (2)

(b) Distance:

h= v₀t + ½ gt²… … … (3)

or, h= 0 + ½ gt²

∴h= ½ gt² … … (4)

(c) Relation between final velocity and distance:

v² = v₀² + 2gh… … … (5)

or, v² = 0 + 2gh

∴ v² = 2gh … … (6)

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

v = v₀ – gt… … … (7)

h= v₀t – ½ gt²… … … (8)

v² = v₀² – 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, v₀

Final velocity at the maximum height v = 0

We know,

v² = v₀² – 2gH

or, 0 = v₀² – 2gH

Time to reach the maximum height:

Let, the time to reach maximum height be = t₁

∴ We get,

v = v₀ – gt₁

or, 0 = v₀ – gt₁

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 t₂

At the maximum height, v = 0

So, using equation (4) we can write

We see from (11) and (12)

t₁ = t₂

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)