A car travels starting form rest with constant acceleration alpha and reaches a maximum velocity V. It travels with maximum velocity for some time and retards uniformly at the rate of beta and the to rest. If s is the total distance and t is the total time of journey then t =

A car travels starting form rest with constant acceleration alpha and

1.	A car travels starting form rest with constant acceleration alpha and reaches a maximum velocity V. It travels with maximum velocity for some time and retards uniformly at the rate of beta and the to rest. If s is the total distance and t is the total time of journey then t =
Answer» Solution : `V=0+ALPHAT,,t_(1)=(v)/(ALPHA)` `S_(1)=(1)/(2)alphat_(1)^(2)=(v^(2))/(2alpha)` `O-V=betat_(3),t_(3)=(v)/(beta)` `O^(2)-V^(2)=-2betaS_(3)` `S_(3)=(v_(2))/(2beta)=(1)/(2)betat_(3)^(2)` `t_(2)=(S_(2))/(V)=(S-(S_(1)+S_(3)))/(V)=(S-(v^(2))/(2)((1)/(alpha)+(1)/(beta)))/(V)` `t=t_(1)+t_(2)+t_(3)` `=(v)/(alpha)+(s)/(v)-(v)/(2alpha)-(v)/(2beta)+(v)/(beta) t=(s)/(v)+(v)/(2)((alpha+beta)/(alphabeta))` `s_(2)=s-(s_(1)+s_(2))=s-((v^(2))/(2alpha)+(v^(2))/(2alpha))` `=s-(v^(2))/(alpha)=s-(vt-s)` `s_(2)=2s-vt` [`S_(2)` = distance TRAVELLED with CONSTANT velocity]