Given, initial speed of engine =u Speed of engine last compartment =v Let the length of train be I and the speed of mid-point of train be v′. Using third equation of motion, v2=u2+2as ⇒v′2=u2+2al∕2 ⇒v′2−u2=al . . . (i) Also, v2−u2=2al⇒a=
v2−u2
2l
Substituting the value of a in Eq. (i), we get v′2−u2=