Question

Write the three equations of motions.

Answer 1

First equation of motion :

1. $\boxed{\bf v = u+at}$

$\bf v = final\:velocity,\: u=initial\:velocity,\:a = acceleration,\: t=time$

Using slope of graph = acceleration

area under graph distance

Second equation of motion :

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

$\bf s=area\:\: under\:\: the \:\:graph\\u=initial \;\:velocity\\t=time\\a=acceleration$

Area under graphs gives the distance covered

$\bf s=area \;\:under\:\:graph\\s= area(ACDB)+area(ACB)\\s=ut+\frac{1}{2}\times t \times (v-u)$

from equation 1 of motion ⇒ v - u = at

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

Third equation of motion :

3. $\boxed{\bf 2as=v^{2}-u^{2}}$

Area under the graph as the direction converted

= area of ABDO

$\bf s=\frac{1}{2}\times (sum\:\:of\:\:parallels) \times height\\\\s=\frac{1}{2}\times (u+v) \times t\\\\s= \frac{1}{2} \times(v+u)\times\frac{(v-u)}{a} \\\\from \:\:eq.1 \rightarrow t=\frac{v-u}{a}\\\\s=\frac{v^{2} - u^{2} }{2a}\\\\s= 2as=v^{2}-u^{2}$

Answer 2

THREE EQUATIONS OF MOTION ARE AS FOLLOWS-

${1}^{st} \: equation \: of \: motion - v = u + at \\ {2}^{nd} \: equation \: of \: motion - s = ut + \frac{1}{2} a {t}^{2} \\ {3}^{rd} \: equation \: of \: motion - {v}^{2} - {u}^{2} = 2as \\ where \\ u = initial \: velocity \\ v = velocity \\ a = acceleration \\ s = distance \\ t = time$