Question

Derive the following equations of motion:

(i) v = u + at

(ii) S = ut + ½ at2

(iii) v2 = u2 + 2aS.

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Answer 1

Explanation:

3. ANSWER

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.

S=ut+21at2andv=u+at, include the time variant t

There will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.

To do this, we rearrange our first equation to get 

t=av−u

and use this to replace t wherever it appears in the second equation. So

S=ut+21at2 becomes,

S=u(av−u)+21a(av−u)2

⇒2aS=2u(v−u)+(v−u)2

⇒2aS=2uv−2u2−v2−2uv−u2

⇒2aS=v2−u2

⇒v2=u2+2aS

Answer 2

$\huge \tt \underline \color{green} \: question \:$

Derive the following equations of motion:

(i) v = u + at

(ii) S = ut + ½ at2

(iii) v2 = u2 + 2aS.

$\huge \tt \underline \color{pink} \: answer \:$

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.

$s = ut + \frac{1}{2} {at}^{2} \: andv = u + at$

include the time variant t

There will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.

To do this, we rearrange our first equation to get

$t = \frac{v - u}{2}$

and use this to replace t wherever it appears in the second equation. So

$s = ut + \frac{1}{2} {at}^{2}$

becomes,

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

$= 2as = 2u(v - u) + ( {v - u)}^{2}$

$= 2as = 2uv - {2u}^{2} - {v}^{2} - 2uv - {u}^{2}$

$= 2as = {v}^{2} - {u}^{2}$

$= {v}^{2} = {u}^{2} + 2as$

Hope it helps......

AKSHITA