A car starts from rest and moves with uniform acceleration a on a straight road from time t=0 to t=T . After that, a constant deceleration brings it to rest. In this process the average speed of the car is
For First part,
u = 0, t = T and acceleration = a
∴ v=0+aT and S1=0+12aT2=12aT2
For second part,
u = aT, retardation = a1, v = 0 and time taken = T1(let)
∴ 0=u−a1T1 ⇒ aT=a1T1
and from v2=u2−2aS2 ⇒S2=u22a1=12 a2T2a1
S2=12aT×T1 (As a1=aTT1)
∴vav=S1+S2T+T1=12aT2+12aT×T1T+T1
=12aT(T+T1)T+T1=12aT