Question

derive the first equation of motion...​

Answer 1

$\huge\tt\underline\purple{Answer:-}$

We know that,

$Acceleration,a=\frac{v–u}{t₁–t₂}$........(I)

Where,

• v – u = change in velocity
• t₁–t₂ = time taken

From equation (I) we get

$➝a=\frac{v–u}{t₁–t₂}$

$➝a=\frac{v–u}{t}$

$➝v–u=at$

$➝v=u+at$

Hence, proved that v = u +at

__________________________

Hope it's help you.....

Answer 2

Let $a=\frac{dv}{dt}$

$a*dt=dv$

Lets integrate both sides

$a*\int\limits^t_0 {} \, dt =\int\limits^v_u {} \, dv$

$a(t-0)=v-u$

$at=v-u$

$v=u+at$  -----required equation