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Explain Ist IInd and IIIrd equation of motion

Answer» First Equation of Motion:The final velocity (v) of a moving object with uniform acceleration (a) after time, t.Let, the initial velocity = u.Final velocity = v.Time = t Acceleration = a________________________________________We know that, Acceleration (a) =Change in velocityTime taken=Change in velocityTime taken⇒a=Final velocity-Initial velocityTime taken⇒a=Final velocity-Initial velocityTime taken⇒a=v−ut⇒a=v-ut⇒at=v−u⇒at=v-u⇒at−v=−u⇒at-v=-u⇒−v=−u−at⇒-v=-u-at⇒v=u+at⇒v=u+at ---(i)This equation is known as first equation of motionSecond Equation of Motion:Distance covered in time (t) by a moving body.Let, Initial velocity of the object = uFinal velocity of the object = vAcceleration = aTime = tDistance covered in given time = sWe know that,Average velocity =Initial velocity+Final velocity2=Initial velocity+Final velocity2∴ Average velocity =u+v2=u+v2 ----(ii)We know that, Distance covered (s) in given time = Average velocity x TimeOr, s = Average velocity x Time -----------------(iii)After substituting the value of average velocity from equation (ii) we get⇒s=u+v2×t⇒s=u+v2×t________________________________________After substituting the value of ‘v’ from first equation of motion we get,⇒s=u+(u+at)2×t⇒s=u+(u+at)2×t⇒s=u+u+at2×t⇒s=u+u+at2×t⇒s=2u+at2×t⇒s=2u+at2×t⇒s=2ut+at22⇒s=2ut+at22⇒s=2ut2+at22⇒s=2ut2+at22⇒s=ut+at22⇒s=ut+at⇒s=ut+12at2⇒s=ut+12at2 ----(iv)The above equation is known as Second equation of motion.Third Equation of Motion:The third equation of motion is derived by substituting the value of time (t) from first equation of motion.We know from first equation of motion, v=u+atv=u+at⇒v−u=at⇒v-u=at⇒at=v−u⇒at=v-u⇒t=v−ua⇒t=v-ua -----(v)__________________________________


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