Question

Derive the second equation of motion!!​

Answer 1

${\bold{\blue{\underline{\red{S}\pink{ol}\green{uti}\purple{on:-}}}}}$

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\red{{2}^{nd}\:equation\:of\:motion}}}}$

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\pink{s=ut+\dfrac{1}{2}a{t}^{2}}}}}$

✎ Let a body moves in a straight path with initial velocity u.

✎ Let the acceleration of the body be a.

✎ v be the velocity of the body of the time t.

✫ Displacement = area of velocity time graph with time axis.

⤤ Displacement = Area of rectangle (▭) OADC + Area of triangle (∆) ABD

$\rm\longrightarrow\:s=OA\times\:OC+\dfrac{1}{2}\times\:AD\times\:BD$

$\rm\longrightarrow\:s=u\times\:t+\dfrac{1}{2}\times\:t\times\:(v-u)$

$\rm\longrightarrow\:s=ut+\dfrac{1}{2}t\times\:(\cancel{u}+at-\cancel{u})$

$\rm\longrightarrow\:s=ut+\dfrac{1}{2}t\times\:at$

$\rm\longrightarrow\:s=ut+\dfrac{1}{2}a{t}^{2}$

Answer 2

Answer:

Derivation of the equation of motion is one of the most important topics in Physics.

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Equations of Motion Formula.

Equations of motionFormulaFirst equation of motionv=u+atSecond equation of motions=ut+\frac{1}{2}at^{2}Third equation of motionv2 = u2+2as