Equations of motion for a uniform accelerated body changing its velocity u to v in time t, with an acceleration a and COVERING a displacement s in the time.v = u + ats = ut + at²/2v² = u² + 2asSolutionLet the initial velocity of the body be u,The body travels with acceleration a₁ for time t₁Final Velocity for this time period is,v = u + a₁t₁Now, The body accelerates with a₂ for time t₂The velocity after this time interval is given,w = v + a₂t₂w = u + a₁t₁ + a₂t₂Average acceleration :It is the change in velocity over the time interval.If velocity changes from a to b over the time interval t,\frac{a - b}{t} = AVG \: acceleration TA−b =avgaccelerationNow Average acceleration is the change in velocity over the entire time interval.Time t = t₁+ t₂Initial velocity = uFinal Velocity = wSo, Average acceleration is,\begin{gathered}= \frac{w - u}{t} \\ \\ = \dfrac{u + a_1t_1+ a_2t_2 - u}{t} \\ \\ = \dfrac{ a_1t_1+ a_2t_2 }{t} \\ \\ = \dfrac{ a_1t_1+ a_2t_2 }{t_1+ t_2}\end{gathered} = tw−u = tu+a 1 t 1 +a 2 t 2 −u = ta 1 t 1 +a 2 t 2 = t 1 +t 2 a 1 t 1 +a 2 t 2 THEREFORE, The average acceleration of the body is\dfrac{ a_1t_1+ a_2t_2 }{t_1+ t_2} \: t 1 +t 2 a 1 t 1 +a 2 t 2