Question

Derive the equation of motion v = u +at, using mathematical method

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• The first equation of motion v = u + at .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Do :- }}}}$

• To derive the first equation of motion by mathematical method.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

We need to derive the first equation of motion by mathematical method . Therefore , let an object has an initial Velocity of u , it accelerates will a acceleration of a , and attains a final velocity of v in time t . So , by the definition of acceleration , we know that the rate of change of velocity is called acceleration . Mathematically ,

$\sf\dashrightarrow a = \dfrac{ v - u}{t} \\\\\\\sf\dashrightarrow a * t = v - u \\\\\\\sf\dashrightarrow v - u = at \\\\\\\sf\dashrightarrow \underset{\blue{\sf First \ Equation }}{\underbrace{\boxed{\pink{\frak{ v = u + at }}}}}$

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MorE To KnoW :-

• The second equation of motion is s = ut + ½at².

• The third equation of motion is 2as = v² - u² .

• The formula to find the distance travelled in nth second is given by $\bf S_n$ = u + ½a( 2n - 1 ) .

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