Question

1. Derive : first equation of motion

Second equation of motion

Third equation of motion


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Answer 1

Answer:

1 st = 2nd - 3rd

Explanation:

try it this way

Answer 2

$\huge \underline \pink{Answer }$

✰ First equation of motion :-

$\bf \red{ \frac{Acceleration \: = \: Change \: in \: velocity \: }{time} }$

$\bf \pink = \pink > \pink a \: \pink= \: \pink \: \frac \pink{v \: - \: u \: }{ \pink t \: }$

$\bf \purple \therefore \displaystyle { \boxed{ \sf { \displaystyle { \purple v \: \purple = \purple u \: \purple + \: \purple a \purple t}}}}$

✰ First Second of motion :-

For uniformly accelerated motion,

$\bf \purple{V_av} \: \purple = \frac{ \purple u \purple+ \purple v}{ \purple2}$

Also, Displacement = (Average velocity) × (Time)

$\bf \green \therefore \: \green s \: \green= \: \green( \frac{ \green u \green+ \green v}{ \green2} \green ) \green \times \green t$

$\bf \orange = \orange > \orange s \: \orange = \: \orange(\frac{ \orange u \orange + \orange a \orange t}{ \orange 2} \orange) \orange t$

$\large \displaystyle { \boxed{ \sf { \displaystyle { \pink s \pink = \pink u \pink \pink \pink + \frac{ \pink1}{ \pink 2} \pink a \pink t \pink ²}}}}$

✰ First Second of motion :-

$\bf \red {F \purple r \pink o\green m } \ (1), \red t \: \green = \frac{ \red v \: \green - \pink u \: }{ \orange a}$

Substituting the value of t in the second equation of motion,

$\bf = > s \: = u( \frac{v - u}{a} ) \: + \: \frac{ 1}{2} a \: ( \frac{v - u}{a})^{2}$

$\bf s \: = > \frac{uv - u ^{2} \: }{a} + \frac{1}{2a} + \frac{ 1}{2} \: ( v^{2} + \: {u}^{2} - 2av \: )$

$\bf = > \frac{2uv - {2u}^{2} + {v}^{2} - 2uv }{2a} = \: \frac{ {v}^{2} \: - {u}^{2} }{2a}$

$\bf \red \therefore \displaystyle { \boxed{ \sf { \displaystyle { \red v ^{ \red2} \: \red = \red {u}^{ \red2} \: \red + \: \red 2 \red a \red s}}}}$

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Thus, the three equations of motion are :

1) v = u + at ‎‎ ‎ this equation does not have s

2) s = ut + $\frac{1}{2}$ at², this equation does not have v

3) v² - u² = 2as this equation does not have t.

The three equations have four physical quantities each.

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