IIT JEE , AIEEE Forum - Physics , Mechanics

Prakriteesh

a = (u2-u1)/T1 = (u3 - u2)/T2 .........................eq(1)

S1 = u1T1 + 1/2. a. T1²

= u1T1 + 1/2 . (u2-u1)/T1 . T1²

= u1T1 - 1/2 . u1T1 + 1/2.u2T1

= 1/2. (u1+u2)T1

So, u1+u2 = 2S1/T1

Also, u2 - u1 = aT1 from eq(1)

Thus u2 + u1 + u2 - u1 = aT1 + 2S1/T1

2u2 = at1 + 2S1/T1

u2 = aT1/2 + S1/T1

Now,

S2 = u2 + 1/2. a. T2²

S2 = (aT1/2 + S1/T1).T2 + 1/2.aT2²

S2 - S1.T2/T1 = aT1.T2/2 + a.T2²/2

So, a = 2{S2T1 - S1T2}/(T1²T2 + T2²T1)

= 2(T1S2 - T2S1) / T1T2(T1+T2)