263Let the body travel a distance a in t1 seconds,a+b in t2 seconds and a+b+c in t3 seconds.Now using average velocity concept in the respective time intervals we get :
a=(v/2)*t1...........(1)
b=v*(t2 - t1).............(2)
c=(v/2)*(t3-t2)........(3)
Also,
v2=2αa...............(4)
v2=2βc............(5)
From (1)-(3) on adding we get
2a +b +2c=v*t3
or,t3=( 2a +b +2c)/v.=T
Now a+b+c=x.............(6)
v/2α=a/v...........(7) [from (4)]
v/2β=c/v.........(8) [frm (5)]
So T=(a+b+c)/v +a/v +c/v
or, T=x/v + v/2α + v/2β
