Question

derive the equation of motion for a particle projected vertically

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Answer 1

Answer:

here the distance or displacement covered is S

but when it's thrown in the air it covers a height then

S equals H

Use 2nd eq of motion

S = ut + 1\2 at^2

Here a = g

H =ut + 1\2 gt^2

Answer 2

Explanation:

Equation of motions for bodies under gravity :

1. V=u+gt -------1

2.s=ut+1/2at²----------2

3.v²-u²=2as----------3

Equations of motion for a particle Falling vertically :

Let us consider an object falling from height with initial velocity u=0 m/s.

The velocity continuously increases as it falls through a height h.

The direction of g and the direction of motion of body are downwards.

Therefore g is taken as positive.

The above equations of motion can be written as :

V=gt-------------4

h=1/2gt²---------5

v²=2gh-------------6

Equations of motion for a body thrown upwards:

When body is projected upwards  with initial velocity =u m/s and it reaches a height h.

Equations of motions can be written as :

v=u-gt----------7

h=ut-1/2gt²-------------8

v²-u²=-2gh--------------9

Hope it helps

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