Explain Ist IInd and IIIrd equation …

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 motion Second Equation of Motion: Distance covered in time (t) by a moving body. Let, Initial velocity of the object = u Final velocity of the object = v Acceleration = a Time = t Distance covered in given time = s We 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 Time Or, 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) __________________________________